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How to Solve a Quadratic Equation By Using the Quadratic Formula

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By Fanof EHow
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A quadratic equation is a polynomial equation of the second degree. It is in the form ax squared+bx+c=0, where a, b, and c are real numbers. It can be solved by factoring, completing the square, or by using the quadratic formula. This article explains how to use the quadratic formula to solve a quadratic equation.

Difficulty: Moderately Easy
Instructions

Things You'll Need:

  • paper
  • pen/pencil
  • calculator
  • quadratic formula
  1. Step 1

    Write out the quadratic equation. It is x=[-b +/- sqrt(b squared-4ac)]/(2a), where x is the root (one of two), a is the coefficient of the x squared term, b is the coefficient of the x term, and c is the constant.

  2. Step 2

    Plug in what you know.

  3. Step 3

    Solve for x. Since it is a quadratic equation, there will be two roots (solutions).

  4. Step 4

    Let's do an example. Solve x squared+3x-10=0 by using the quadratic formula. Here, a=1 (since there is no written coefficient), b=3, and c=-10. Write out the formula: x=[-b +/- sqrt(b squared-4ac)]/2a and plug in the numbers. x=[-3 +/- sqrt(3 squared -4(1)(-10) which simplifies to x=[-3 +/- sqrt(9-(-40))]/2 or [-3 +/- 7]/2. x=-5 or x=2.

Tips & Warnings
  • Be careful with plus and minus signs, especially under the radical sign.
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