Question

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

Answer 1

• lesser x = -1.84
• lesser x = -8.16

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)=√(f\left(a\right)),\:\:-√(f\left(a\right))`

solve

`x+5=√(10)`

Subtract 5 from both sides

`x+5-5=√(10)-5`

`x=√(10)-5`

`x=-1.8`

so

`x+5=-√(10)`

Subtract 5 from both sides

`x+5-5=-√(10)-5`

Simplify

`x=-√(10)-5`

`\:x=-8.2`

As -1.84 > -8.16

so

• lesser x = -1.84
• lesser x = -8.16