The method used for finding the solution(s)of quadratic equations in this lesson is to factor the quadratic expression and then use the Zero Product Property.
In order to solve a quadratic equation by factoring, the equation has to be written in standard form. The equation 2x2 + 7x = -3 has been rewritten into standard form below.
2x2 + 7x = -3
2x2 + 7x + 3 = 0
Once the equation is in standard form, factor the quadratic expression.
2x2 + 7x + 3 = 0
(2x + 1)(x + 3) = 0
Using the Zero Product Property set each factor equal to 0 and solve for x.
| 2x + 1 = 0 | |
| 2x + 1 - 1 = 0 - 1 | x + 3 = 0 |
| 2x = -1 | x + 3 - 3 = 0 - 3 |
| 2x 2 = -1 2 | x = -3 |
| x = -1 2 |
The solutions to the equation are -1 2 and -3.