How to Use the Quadratic Formula to Solve a Quadratic Equation

By Contributor
The quadratic formula is one way to solve algebra equations.

More advanced algebra classes will require you to solve all kinds of different equations. To solve an equation in the form ax^2 + bx + c = 0, where "a" is not equal to zero, you can employ the quadratic formula. Indeed, you can use the formula to solve any second-degree equation. The task consists of plugging numbers into the formula and simplifying.

Write down the quadratic formula on a piece of paper: x = [-b +/- √(b^2 - 4ac)] / 2a.

Choose a sample problem to solve. For example, consider 6x^2 + 7x - 20 = 0. Compare the coefficients in the equation to the standard form, ax^2 + bx + c = 0. You'll see that a = 6, b = 7 and c = -20.

Plug the values you found in Step 2 into the quadratic formula. You should obtain the following: x = [-7 +/- √(7^2 - 4_6_-20)] / 2*6.

Solve the portion inside the square root sign. You'll should obtain 49 - (-480). This is the same as 49 + 480, so the result is 529.

Calculate the square root of 529, which is 23. Now you can determine the numerators: -7 + 23 or -7 - 23. So your result will have a numerator of 16 or - 30.

Calculate the denominator of your two answers: 2*6 = 12. So your two answers will be 16/12 and -30/12. By dividing by the largest common factor in each, you obtain 4/3 and -5/2.

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