Question

What is the solution to the equation below?

x+4=√8-x
A. x=0
B. x=-1
C. x=-7
D. x=4

Answer 1

Explanation:

`x+4=√(8-x) \\squaring\\x^(2) +8x+16=8-x\\x^(2) +8x+x+16-8=0\\x^(2) +9x+8=0\\x^(2) +x+8x+x=0\\x(x+1)+8(x+1)=0\\(x+1)(x+8)=0\\either \\x+1=0,\\x=-1\\or\\x+8=0\\x=-8\\x=-8 ~is~ an~ extraneous~ solution \\as~-8+4=√(8+8) \\-4=√(16) \\-4=4\\`

it does not satisfy the given equation.

Hence rejected.

so solution is x=-1