Question

Krzysztof solved the quadratic equation $11x^2-44x-99=0$ by completing the square. In the process, he came up with the equivalent equation (x+r)^2 = s, where $r$ and $s$ are constants. What is $r+s$?

Answer 1

Dividing both sides of the equation by , we have The square which agrees with except for the constant term is , which is equal to and thus to .Therefore, by adding to each side, Krzysztof rewrote the equation as We have -2 and 13 and therefore our answer is 11

Answer 2

r = -2

s = 13

Explanation:

Given quadratic equation is,

11x² - 44x - 99 = 0

Divide this equation by 11,

x² - 4x - 9 = 0

x² - 2(2)x - 9 = 0

x² -2(2)x + 2² - 2² - 9 = 0

[x² - 2(2)x + 2²] - 4- 9 = 0

(x - 2)² - 13 = 0

(x - 2)² = 13

[x + (-2)]² = 13

By comparing this equation with (x + r)² = s

Values of the constants r and s will be,

r = (-2) and s = 13