[tex]x^{2} +6^{2} = (x+6)^{2} \\ x^{2} +36=( x+6)^{2} [/tex]
First, on the right side of the equation, you want to square the binomial (x+6). To do this, write it out like this:
[tex] x^{2} + 36 = (x+6)(x+6) [/tex]
Then, FOIL out the two binomials on the right. To do this, you multiply the first terms, the outermost terms, the innermost terms, and the last terms:
[tex] x^{2} + 36 = (x*x)+(x*6)+(x*6)+(6*6)[/tex]
Then, simplify and combine like terms on the right side:
[tex] x^{2} + 36 = x^{2} +6x+6x+36 \\ x^{2} +36= x^{2} +12x+36[/tex]
After that, subtract 36 from both sides. Then, subtract x² from both sides:
[tex]( x^{2} +36)-36= ( x^{2} +12x+36)-36 \\ x^{2} = x^{2} +12x \\ ( x^{2})- x^{2} =( x^{2} +12x)- x^{2} \\ 0=12x[/tex]
Finally, divide each side by 12 to isolate x:
[tex](0)/12=(12x)/12 \\ x=0[/tex]
Your answer is x=0.
Hope this helps!
