Question

Solve for x. Enter the solutions from least to greatest. (x+15)^2-10=0

Answer 1

Answer:

• lesser x = -1.84
• lesser x = -8.16

Step-by-step explanation:

Given the expression

$\left(x+5\right)^2-10=0$

Add 10 to both sides

$\left(x+5\right)^2-10+10=0+10$

Simplify

$\left(x+5\right)^2=10$

$\mathrm{For\:}\left(g\left(x\right)\right)^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}g\left(x\right)=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}$

solve

$x+5=\sqrt{10}$

Subtract 5 from both sides

$x+5-5=\sqrt{10}-5$

$x=\sqrt{10}-5$

$x=-1.8$

so

$x+5=-\sqrt{10}$

Subtract 5 from both sides

$x+5-5=-\sqrt{10}-5$

Simplify

$x=-\sqrt{10}-5$

$\:x=-8.2$

As -1.84 > -8.16

so

• lesser x = -1.84
• lesser x = -8.16