The answer is 6^2 or 36.
Steps:
Subtract x + 36 from both sides
x-12 √x+36-(x+36)=0-(x+36)-12 √x=-x-36Square both sides (-12 √x)^2=(-x-36)^2Expand (-12 √x)^2: 144x(-12 √x)^2Apply exponent rule (-a)^n=a^n if n is even(-12 √x)^2=(12 √x)^2Apply exponent rule (a*b)^n=a^n b^n=12^2( √x)^2 (
√x)^2:x
√a=a^1/2
=(x^1/2)^2
Apply exponent rule (a^b)^c=a^bc
=x^1/2*2
1/2*2=1
1/2*2
Multiply Fractions a*b/c=a*b/c
=1*2/2
Apply rule 1*a=a
2/2
Cancel out common factor 2
=1
=x
=12^2x
12^2=144
=144x
Expand (-x-36)^2: x^2+72x+1296
(-x-36)^2
Apply distributing rule (a-b)^2=a^2-2ab+b^2
a=-x,b=36
=(-x)^2-2(-x)*36+36^3
Simplify (-x)^2-2(-x)*36+36^2: x^2+72x+1296
(-x)^2-2(-x)*36+36^2
Apply rule -(-a)=a
=(-x)^2+2x*36+36^2
Apply exponent rule (-a)^n=a^n if n is even
(-x)^2=x^2
=x^2+2*36x+36^2
Refine
=x^2+72x+1296
144x=x^2+72x+1296
Solve 144x=x^2+72x+1296: x = 36
144x=x^2+72x+1296
Switch sides
x^2+72x+1296=144x
Subtract 144x from both sides
x^2+72x+1296-144x=144x-144x
Simplify
x^2-72x+1296=0
(-72)^2-4*1*1296=0
(-72)^2-4*1*1296
Apply exponent rule (-a)^n=a^n,if n is even
(-72)^2 = 72^2
=72^2-1*4*1296
Multiply the numbers 4*1*1296=5184
=72^2-5184
72^2=5184
5184-5184
=0
x1,2=-(-72)+/ √0 / 2*1
x = -(-72)/2*1
-(-72)/2*1=36
-(-72)/2*1
Multiply the numbers 2*1 = 2
=72/2
=36
x = 36
6^2 = 36
6^2 = 6*6
6*6=36
Answer: 6^2
Hope this helps you! (:
-Hamilton1757
