Solve x^2+12^2=left(x+9right)^2

$${ x }^{ 2 } + { 12 }^{ 2 } = { \left(x+9 \right) }^{ 2 }$$

Solve for x

$$x = \frac{7}{2} = 3\frac{1}{2} = 3.5$$

Steps for Solving Linear Equation

Calculate 12 to the power of 2 and get 144.

$$x^{2}+144=\left(x+9\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+9\right)^{2}.

$$x^{2}+144=x^{2}+18x+81$$

Subtract x^{2} from both sides.

$$x^{2}+144-x^{2}=18x+81$$

Combine x^{2} and -x^{2} to get 0.

$$144=18x+81$$

Swap sides so that all variable terms are on the left hand side.

$$18x+81=144$$

Subtract 81 from both sides.

$$18x=144-81$$

Subtract 81 from 144 to get 63.

$$18x=63$$

Divide both sides by 18.

$$x=\frac{63}{18}$$

Reduce the fraction \frac{63}{18} to lowest terms by extracting and canceling out 9.

$$x=\frac{7}{2}$$