Answer:
[tex]x=\sqrt{26}-4,\:x=-\sqrt{26}-4[/tex]
Step-by-step explanation:
[tex]x^2+8x=10[/tex]
Write this equation in the form of: [tex]x^2+2ax+a^2=\left(x+a\right)^2[/tex]
Solve for a:
[tex]2ax=8x[/tex]
[tex]\frac{2ax}{2x}=\frac{8x}{2x}[/tex]
[tex]a=4[/tex]
Add [tex]a^2=4^2[/tex] to both sides:
[tex]x^2+8x+4^2=10+4^2[/tex]
[tex]\left(x+4\right)^2=26[/tex]
[tex]x+4=\sqrt{26}[/tex]
[tex]x+4-4=\sqrt{26}-4[/tex]
[tex]x=\sqrt{26}-4[/tex]
[tex]x+4=-\sqrt{26}[/tex]
[tex]x+4-4=-\sqrt{26}-4[/tex]
[tex]x=-\sqrt{26}-4[/tex]
