How to Use the Quadratic Formula to Solve a Quadratic Equation

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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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