### Home > CCA2 > Chapter 12 > Lesson 12.1.1 > Problem12-19

12-19.

Solve each equation.

1. $\sqrt { x + 7 }+ 5 = x$

Subtract $5$ from both sides to isolate the radical.

$\sqrt{x+7}\ =\ x-5$

Square both sides to get rid of the radical sign.

$x+7\ =\ x^2-10x+25$

Set the equation equal to $0$ and use the Quadratic Formula to solve for $x$.

1. $\frac { a } { a ^ { 2 } - 36 } + \frac { 2 } { a - 6 } = \frac { 1 } { a + 6 }$

What are the factors of $a^2 - 36?$ Multiply both sides of the equation by a common denominator to remove the fractions.

$a = -9$