Question

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

Answer 1

7 and -8

Explanation:

Square both sides -->
`9x + 81 = (x + 5)^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.