How to Solve Quadratic Equations by Factoring
- 1
3x^2 - 20x = 7 = 0
Convert the equation to quadratic form (ax^2 + bx + c = 0), if it has not been converted already. This article will be using the problem 3x^2 - 20x = 7 as an example. Subtract 7 from both sides, so that your equation becomes 3x^2 - 20x = 7 = 0. - 2
3x^2 - 20x - 7
Remove the '0' so that your equation now simply reads 3x^2 - 20x - 7. - 3
(3x + 1)(x - 7)
Factor the equation. Since bx & c are both negative, (-20x & -7), we know we must have one factor with a positive and one with a negative. That means our base would be (3x + )(x - ). Because 3x times 7 = 21x, we know we must put 7 in the second factor, because that is the closest number to 20x. That means our factored equation is (3x + 1)(x - 7). - 4
x = -1/3
Take the first factor (3x + 1), remove the parentheses and add '0' to the end, leaving you with 3x + 1 = 0. Now solve this problem like any other basic equation. Subtract 1 from both sides so that you have 3x = -1. Divide both sides by 3, leaving you with x = -1/3. - 5
x = 7
Take the second factor, remove the parentheses and add '0' to the end, leaving you with x - 7 = 0. Add 7 to both sides, leaving you with x = 7. This means that the answer to your quadratic equation is x = -1/3 or x = 7.
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