Solve (x+6)^2=(15-x)^2

$$( x + 6 ) ^ { 2 } = ( 15 - x ) ^ { 2 }$$

Solve for x

$$x = \frac{9}{2} = 4\frac{1}{2} = 4.5$$

Steps for Solving Linear Equation

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+6\right)^{2}.

$$x^{2}+12x+36=\left(15-x\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(15-x\right)^{2}.

$$x^{2}+12x+36=225-30x+x^{2}$$

Add 30x to both sides.

$$x^{2}+12x+36+30x=225+x^{2}$$

Combine 12x and 30x to get 42x.

$$x^{2}+42x+36=225+x^{2}$$

Subtract x^{2} from both sides.

$$x^{2}+42x+36-x^{2}=225$$

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

$$42x+36=225$$

Subtract 36 from both sides.

$$42x=225-36$$

Subtract 36 from 225 to get 189.

$$42x=189$$

Divide both sides by 42.

$$x=\frac{189}{42}$$

Reduce the fraction \frac{189}{42} to lowest terms by extracting and canceling out 21.

$$x=\frac{9}{2}$$