## anonymous 4 years ago identify the solutions to the equation when you solve by completing the square

1. anonymous

|dw:1327792597382:dw|

2. Rogue

$x ^{2} - 5x = 24$ For a quadratic equation$ax ^{2} + bx + c = 0$ When solving by completing the square, you must bring C to the other side first, which is already done for your equation. Next up must add $\frac {b^{2}}{4}$ to both sides. In your case, $\frac {b^{2}}{2} = \frac {-5^{2}}{2} = \frac {25}{2}$ Adding that do both sides of the equation, we get$x ^{2} - 5x + \frac {25}{4} = 24 + \frac {25}{4}$ We see that we can factor this into:$(x - \frac {5}{2})^{2} = 24 + \frac {25}{4} = \frac {121}{4}$ We can square root both sides to get$(x-\frac {5}{2}) = \pm \sqrt{\frac {121}{4}}$ Now we just add 5/2 to both sides and we get that$x = \frac {5}{2} \pm \sqrt{\frac {121}{4}}$ If we simplify that further, we get$x = \frac {5}{2} \pm \frac {11}{2} = \frac {5 \pm 11}{2}$ The two solutions are then:$x = \frac {5 + 11}{2} = 8$$x = \frac {5 - 11}{2} = -3$