Answer:
[tex]x = - 1 + 2 \sqrt{3} [/tex]
[tex]x = - 1 - 2 \sqrt{3} [/tex]
Step-by-step explanation:
[tex] {x}^{2} + 2x - 8= 3[/tex]
[tex] {x}^{2} + 2x = 11[/tex]
Complete the square
[tex] (\frac{2}{2} ) {}^{2} = 1[/tex]
so
[tex] {x}^{2} + 2x + 1 = 11 + 1[/tex]
[tex] {x}^{2} + 2x + 1 = 12[/tex]
[tex]( x + 1) {}^{2} = 12[/tex]
[tex]x + 1 = \sqrt{12} [/tex]
[tex]x = - 1 + \sqrt{12} [/tex]
or
[tex]x + 1 = - \sqrt{12} [/tex]
[tex]x = - 1 - \sqrt{12} [/tex]
If you want it simplified, you could say
