Question

`√(x + 12) = x+5`

Answer 1

We can solve the equation that has square root by completing the square (The purpose is to get rid of the square root.)

From
`√(x+12)=x+5`

Completing the square for both sides.

`(√(x+12))^2=(x+5)^2\\x+12=x^2+10x+25\\x^2+10x+25-x-12=0\\x^2+9x+13=0`

Because this polynomial cannot be factored. We have to use the Quadratic Formula to solve the equation.

`x=-(b±√(b^2-4ac) )/(2a)`

`x=(-9±√(9^2-4(1)(13)) )/(2)\\x=(-9±√(81-52) )/(2)\\x=(-9±√(29) )/(2)`

But from the graph, the radical function graph doesn't intercept y = x+5 at (-9+√29)/2

Therefore, the answer is (-9-√29)/2

Also Ignore A' in the Quadratic Formula. It appears there whenever I want to put "plus-minus" symbol in the formula.