Answer:
- lesser x = -1.84
- lesser x = -8.16
Step-by-step explanation:
Given the expression
[tex]\left(x+5\right)^2-10=0[/tex]
Add 10 to both sides
[tex]\left(x+5\right)^2-10+10=0+10[/tex]
Simplify
[tex]\left(x+5\right)^2=10[/tex]
[tex]\mathrm{For\:}\left(g\left(x\right)\right)^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}g\left(x\right)=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}[/tex]
solve
[tex]x+5=\sqrt{10}[/tex]
Subtract 5 from both sides
[tex]x+5-5=\sqrt{10}-5[/tex]
[tex]x=\sqrt{10}-5[/tex]
[tex]x=-1.8[/tex]
so
[tex]x+5=-\sqrt{10}[/tex]
Subtract 5 from both sides
[tex]x+5-5=-\sqrt{10}-5[/tex]
Simplify
[tex]x=-\sqrt{10}-5[/tex]
[tex]\:x=-8.2[/tex]
As -1.84 > -8.16
so
- lesser x = -1.84
- lesser x = -8.16
