Go to Factoring, enter the equation x2 + 8x + 16 = 0 into the box and click "Factor".
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.
Check the solutions in the original equation.
| 2x2 + 7x = -3 | 2x2 + 7x = -3 |
| 2(- 1 2 )2 + 7(- 1 2 ) = -3 | 2(-3)2 + 7(-3) = -3 |
| 2( 1 4 ) - 7 2 = -3 | 2(9) - 21 = -3 |
| 1 2 -3 1 2 = -3 | 18 - 21 = -3 |
| -3 = -3 | -3 = -3 |
Example: Solve: x2 + 8x + 16 = 0
x2 + 8x + 16 = 0
(x + 4)(x + 4) = 0
Since the two factors of the quadratic expression are the same, the equation has only one real root.
x + 4 = 0
x + 4 - 4 = 0 - 4
x = -4
Check the solution.
x2 + 8x + 16 = 0
(-4)2+ 8(-4) + 16 = 0
16 - 32 + 16 = 0
-16 + 16 = 0
0 = 0
Go to Factoring, enter the equation x2 + 8x + 16 = 0 into the box and click "Factor".