Question

Solve for x. Write the smaller solution first, and the larger solution second.

(x+7)^2 - 11 = 0

smaller x =
larger x =

Answer 1

Please see that you don't have to solve the quadratic equation to get the answer. You can do it in a very simple way as follows:

${(x + 7)}^{2} - 11 = 0 \\ \\ \Rightarrow {(x + 7)}^{2} = 11 \\ \\ \Rightarrow x + 7 = \pm \sqrt{11} \\ \\ \Rightarrow x = - 7 \pm \sqrt{11} \\ \\ smaller \: x = - 7 - \sqrt{11} \\ \\ larger \: x = - 7 + \sqrt{11}$