# How do you solve sqrt( 9x+81)= x+5?

Apr 26, 2016

7 and -8

#### Explanation:

Square both sides -->
$9 x + 81 = {\left(x + 5\right)}^{2} = {x}^{2} + 10 x + 25.$
${x}^{2} + x - 56 = 0.$
Solve this quadratic equation by using the new Transforming Method (Socratic Search).
Find 2 numbers knowing sum (-1) and product (-56).
The roots have opposite signs because ac < 0.
Factor pairs of (-56) --> ...(-7, 8)(7, -8). This last sum is -1 = -b. Then, the 2 real roots are: 7 and -8.