Question

$\sqrt{x + 12} = x+5$

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 $\sqrt{x+12}=x+5$

Completing the square for both sides.

$(\sqrt{x+12})^2=(x+5)^2\\x+12=x^2+10x+25\\x^2+10x+25-x-12=0\\x^2+9x+13=0$

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

$x=-\frac{b±\sqrt{b^2-4ac} }{2a}$

$x=\frac{-9±\sqrt{9^2-4(1)(13)} }{2}\\x=\frac{-9±\sqrt{81-52} }{2}\\x=\frac{-9±\sqrt{29} }{2}$

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.