Question

Given the function y = x2 + 2x - 8, what are the values of x when y = 3?

Answer 1

Answer:

$x = - 1 + 2 \sqrt{3}$

$x = - 1 - 2 \sqrt{3}$

Step-by-step explanation:

${x}^{2} + 2x - 8= 3$

${x}^{2} + 2x = 11$

Complete the square

$(\frac{2}{2} ) {}^{2} = 1$

so

${x}^{2} + 2x + 1 = 11 + 1$

${x}^{2} + 2x + 1 = 12$

$( x + 1) {}^{2} = 12$

$x + 1 = \sqrt{12}$

$x = - 1 + \sqrt{12}$

or

$x + 1 = - \sqrt{12}$

$x = - 1 - \sqrt{12}$

If you want it simplified, you could say