Verified answer

You're off to an excellent start. From here:

x^2 + x - 56 = 0

you need to solve the quadratic in whatever method you know. In this case, it can be factored:

(x - 7)(x + 8) = 0

x = 7 or -8

You also need to check your answers in the original equation. If you try x = 7, you'll see that it works. If you try x = -8, you'll see that it doesn't (especially since the right hand side would be negative, and the left hand side is positive). So, the only solution is x = 7.

1) Square root both sides.

9x+81 = (x+5)^2

2) Expand and collect liked terms.

9x + 81 = x^2 + 10x + 25

x^2 + 10x + 25 - 9x - 81 = 0

3) Simplify.

x^2 + 10x + 25 - 9x - 81 = x^2 + x - 56

4) Set the right side of the equation to zero and factor.

x^2 + x - 56 = 0

(x - 7) (x + 8) = 0

5) Set each of the two binomials equal to zero and solve for x.

(x - 7) = 0

x = 7

(x + 8) = 0

x = - 8

6) Since there are two binomials containing the variable x, you shall calculate two possible values for x. So: x = 7, and x = - 8

I don't know the whole answer but I got part of this solved,

9X+81=(X+5) (X+5)

9X+81=X^2+5X+5X+25

81-25=X^2+10X-9X

56=X^2+X

That's all I got, X squad plus X equals 56,

I suppose you have to bring in logarithms to solve the rest of this but I'm not familiar in that area.

√(9x + 81) = x + 5

9x + 81 = (x + 5)(x + 5)

9x + 81 = x^2 + 10x + 25

0 = x^2 + x - 56

0 = (x + 8)(x - 7)

x = {-8, 7}

check for extraneous solutions

√(9*-8 + 81) = -8 + 5

√9 = -3

3 = -3

-8 is NOT a solution

√(9*7 + 81) = 7 + 5

√144 = 12

12 = 12

x = 7