Solve the equation by the square root property calculator

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Quadratic Formula Calculator

What do you want to calculate?

Example: 2x^2-5x-3=0

Step-By-Step Example

Learn step-by-step how to use the quadratic formula!


Example (Click to try)

2x2−5x−3=0


About the quadratic formula

Solve an equation of the form ax2+bx+c=0 by using the quadratic formula:

x=

−b±√b2−4ac
2a

Quadratic Formula Video Lesson

Solve the equation by the square root property calculator

Solve with the Quadratic Formula Step-by-Step [1:29]

Need more problem types? Try MathPapa Algebra Calculator

Example: 3x^2-2x-1=0

Step-By-Step Example

Learn step-by-step how to solve quadratic equations!

Example (Click to try)


Choose Your Method

There are different methods you can use to solve quadratic equations, depending on your particular problem.

Solve By Factoring

Example: 3x^2-2x-1=0

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

Example: 2x^2=18

Quadratic Formula

Example: 4x^2-2x-1=0

About quadratic equations

Quadratic equations have an x^2 term, and can be rewritten to have the form: ax2+bx+c=0

Need more problem types? Try MathPapa Algebra Calculator

Calculator Use

This calculator is a quadratic equation solver that will solve a second-order polynomial equation in the form ax2 + bx + c = 0 for x, where a ≠ 0, using the completing the square method.

The calculator solution will show work to solve a quadratic equation by completing the square to solve the entered equation for real and complex roots.

Completing the square when a is not 1

To complete the square when a is greater than 1 or less than 1 but not equal to 0, factor out the value of a from all other terms.

For example, find the solution by completing the square for:

\( 2x^2 - 12x + 7 = 0 \)

\( a \ne 1, a = 2 \) so divide through by 2

\( \dfrac{2}{2}x^2 - \dfrac{12}{2}x + \dfrac{7}{2} = \dfrac{0}{2} \)

which gives us

\( x^2 - 6x + \dfrac{7}{2} = 0 \)

Now, continue to solve this quadratic equation by completing the square method.

Completing the square when b = 0

When you do not have an x term because b is 0, you will have a easier equation to solve and only need to solve for the squared term.

For example: Solution by completing the square for:

\( x^2 + 0x - 4 = 0 \)

Eliminate b term with 0 to get:

\( x^2 - 4 = 0 \)

Keep \( x \) terms on the left and move the constant to the right side by adding it on both sides

\( x^2 = 4\)

Take the square root of both sides

\( x = \pm \sqrt[]{4} \)

therefore

\( x = + 2 \)

\( x = - 2 \)

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How do you solve a square root equation step by step?

To isolate the radical, subtract 1 from both sides. Simplify. Square both sides of the equation..
Isolate the radical on one side of the equation..
Raise both sides of the equation to the power of the index..
Solve the new equation..
Check the answer in the original equation..

What is the square √ 64?

The square root of 64 is 8, i.e. √64 = 8. The radical representation of the square root of 64 is √64. Also, we know that the square of 8 is 64, i.e. 82 = 8 × 8 = 64. Thus, the square root of 64 can also be expressed as √64 = √(8)2 = √(8 × 8) = 8.

What is the square root property example?

The definition of the square root of a positive real number in symbol form is if x2 = a, then x = ±√a. For example, the square root of 64 is ±8, because 8∙8 is 64 and -8∙-8 is also 64. Suppose that y2 = b. Using substitution, y = ±√b.