Quadratic Equation Solver
What do you want to calculate.
- Solve for Variable
- Practice Mode
Example (click to try), choose your method, solve by factoring.
Complete The Square
Example: 3x^2-2x-1=0 (After you click the example, change the Method to 'Solve By Completing the Square'.)
Take the Square Root
Quadratic Equation Calculator
Solve quadratic equations step-by-step.
- One-Step Addition
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Frequently Asked Questions (FAQ)
How do you calculate a quadratic equation.
- To solve a quadratic equation, use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a).
What is the quadratic formula?
- The quadratic formula gives solutions to the quadratic equation ax^2+bx+c=0 and is written in the form of x = (-b ± √(b^2 - 4ac)) / (2a)
Does any quadratic equation have two solutions?
- There can be 0, 1 or 2 solutions to a quadratic equation. If the discriminant is positive there are two solutions, if negative there is no solution, if equlas 0 there is 1 solution.
What is quadratic equation in math?
- In math, a quadratic equation is a second-order polynomial equation in a single variable. It is written in the form: ax^2 + bx + c = 0 where x is the variable, and a, b, and c are constants, a ≠ 0.
How do you know if a quadratic equation has two solutions?
- A quadratic equation has two solutions if the discriminant b^2 - 4ac is positive.
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Quadratic Formula Calculator
This online calculator is a quadratic equation solver that will solve a second-order polynomial equation such as ax 2 + bx + c = 0 for x, where a ≠ 0, using the quadratic formula .
The calculator solution will show work using the quadratic formula to solve the entered equation for real and complex roots. Calculator determines whether the discriminant \( (b^2 - 4ac) \) is less than, greater than or equal to 0.
When \( b^2 - 4ac = 0 \) there is one real root.
When \( b^2 - 4ac > 0 \) there are two real roots.
When \( b^2 - 4ac < 0 \) there are two complex roots.
The quadratic formula
is used to solve quadratic equations where a ≠ 0 (polynomials with an order of 2)
Examples using the quadratic formula
Example 1: Find the Solution for \( x^2 + -8x + 5 = 0 \), where a = 1, b = -8 and c = 5, using the Quadratic Formula.
The discriminant \( b^2 - 4ac > 0 \) so, there are two real roots.
Simplify the Radical:
Simplify fractions and/or signs:
Example 2: Find the Solution for \( 5x^2 + 20x + 32 = 0 \), where a = 5, b = 20 and c = 32, using the Quadratic Formula.
The discriminant \( b^2 - 4ac < 0 \) so, there are two complex roots.
calculator updated to include full solution for real and complex roots
Cite this content, page or calculator as:
Furey, Edward " Quadratic Formula Calculator " at https://www.calculatorsoup.com/calculators/algebra/quadratic-formula-calculator.php from CalculatorSoup, https://www.calculatorsoup.com - Online Calculators
Quadratic Equation Solver
Is it quadratic.
Only if it can be put in the form ax 2 + bx + c = 0 , and a is not zero .
The name comes from "quad" meaning square, So, the biggest clue is that highest power must be a square (in other words x 2 ).
These are all quadratic equations in disguise:
How does this work?
The solution(s) to a quadratic equation can be calculated using the Quadratic Formula :
The "±" means you need to do a plus AND a minus, so there are normally TWO solutions !
The blue part ( b 2 - 4ac ) is called the "discriminant", because it can "discriminate" between the possible types of answer. If it is positive, you will get two normal solutions, if it is zero you get just ONE solution, and if it is negative you get imaginary solutions.
Quadratic Formula Calculator
Enter the equation you want to solve using the quadratic formula.
The Quadratic Formula Calculator finds solutions to quadratic equations with real coefficients. For equations with real solutions, you can use the graphing tool to visualize the solutions.
Quadratic Formula : x = − b ± b 2 − 4 a c 2 a
Click the blue arrow to submit. Choose "Solve Using the Quadratic Formula" from the topic selector and click to see the result in our Algebra Calculator !
Solve Using the Quadratic Formula Apply the Quadratic Formula
Solve Using the Quadratic Formula x 2 + 5 x + 6 = 0 Solve Using the Quadratic Formula x 2 - 9 = 0 Solve Using the Quadratic Formula 5 x 2 - 7 x - 3 = 0 Apply the Quadratic Formula x 2 - 14 x + 49 Apply the Quadratic Formula x 2 - 18 x - 4
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Quadratic Formula Calculator
The calculator below solves the quadratic equation of ax 2 + bx + c = 0 .
In algebra, a quadratic equation is any polynomial equation of the second degree with the following form:
ax 2 + bx + c = 0
where x is an unknown, a is referred to as the quadratic coefficient, b the linear coefficient, and c the constant. The numerals a , b , and c are coefficients of the equation, and they represent known numbers. For example, a cannot be 0, or the equation would be linear rather than quadratic. A quadratic equation can be solved in multiple ways, including factoring, using the quadratic formula, completing the square, or graphing. Only the use of the quadratic formula, as well as the basics of completing the square, will be discussed here (since the derivation of the formula involves completing the square). Below is the quadratic formula, as well as its derivation.
Derivation of the Quadratic Formula
From this point, it is possible to complete the square using the relationship that:
x 2 + bx + c = (x - h) 2 + k
Continuing the derivation using this relationship:
Recall that the ± exists as a function of computing a square root, making both positive and negative roots solutions of the quadratic equation. The x values found through the quadratic formula are roots of the quadratic equation that represent the x values where any parabola crosses the x-axis. Furthermore, the quadratic formula also provides the axis of symmetry of the parabola. This is demonstrated by the graph provided below. Note that the quadratic formula actually has many real-world applications, such as calculating areas, projectile trajectories, and speed, among others.
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Quadratic Formula Calculator & Solver
Calculator for solutions to any quadratic equation..
The calculator uses the quadratic formula to find solutions to any quadratic equation .
The quadratic formula calculator below will solve any quadratic equation that you type in. Simply type in a number for 'a', 'b' and 'c' then hit the 'solve' button.
Quadratic Formula Calculator and Solver
The Actual Solutions
Parabola Animated Gifs
More Quadratic Gifs
The calculator on this page shows how the quadratic formula operates, but if you have access to a graphing calculator you should be able to solve quadratic equations, even ones with imaginary solutions.
- Step 1) Most graphing calculators like the TI- 83 and others allow you to set the "Mode" to "a + bi" (Just click on 'mode' and select 'a+bi').
- If you can set your calculator's mode to a + bi you should be able to even calculate imaginary solutions.
- The rest of the steps just involve typing in a,b and c. Make sure that you divide the entire numerator by 2a, just use parentheses.
- Quadratic formula worksheets (several free printable pdfs with answer keys on the quadratic formula)
Create the graph of any Parabola
Save Graph as Image to your desktop
- Quadratic Equations
- Other Free Math Calculators
- All roots calculated
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