Answer:
The correct options for the solution values are:
- [tex]x=-2\sqrt{2}-5[/tex]
Step-by-step explanation:
Given the expression
[tex]x^2+10x+25=8[/tex]
Subtract 25 from both sides
[tex]x^2+10x+25-25=8-25[/tex]
Simplify
[tex]x^2+10x=-17[/tex]
Add 25 or 5² to both sides
[tex]x^2+10x+5^2=8[/tex]
as
[tex]x^2+10x+5^2=\left(x+5\right)^2[/tex]
so the expression becomes
[tex]\left(x+5\right)^2=8[/tex]
[tex]\mathrm{For\:}f^2\left(x\right)=a\mathrm{\:the\:solutions\:are\:}f\left(x\right)=\sqrt{a},\:-\sqrt{a}[/tex]
solve
[tex]x+5=\sqrt{8}[/tex]
Subtract 5 from both sides
[tex]x+5-5=2\sqrt{2}-5[/tex]
[tex]x=2\sqrt{2}-5[/tex]
solve
[tex]x+5=-\sqrt{8}[/tex]
Subtract 5 from both sides
[tex]x+5-5=-2\sqrt{2}-5[/tex]
[tex]x=-2\sqrt{2}-5[/tex]
Therefore, the solution to the equation
[tex]x=2\sqrt{2}-5,\:x=-2\sqrt{2}-5[/tex]
Hence, the correct options for the solution values are:
- [tex]x=-2\sqrt{2}-5[/tex]
