Solve left(x-8right)^2=left(7-xright)^2

$${ \left(x-8 \right) }^{ 2 } = { \left(7-x \right) }^{ 2 }$$

Solve for x

$$x = \frac{15}{2} = 7\frac{1}{2} = 7.5$$

Steps for Solving Linear Equation

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-8\right)^{2}.

$$x^{2}-16x+64=\left(7-x\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(7-x\right)^{2}.

$$x^{2}-16x+64=49-14x+x^{2}$$

Add 14x to both sides.

$$x^{2}-16x+64+14x=49+x^{2}$$

Combine -16x and 14x to get -2x.

$$x^{2}-2x+64=49+x^{2}$$

Subtract x^{2} from both sides.

$$x^{2}-2x+64-x^{2}=49$$

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

$$-2x+64=49$$

Subtract 64 from both sides.

$$-2x=49-64$$

Subtract 64 from 49 to get -15.

$$-2x=-15$$

Divide both sides by -2.

$$x=\frac{-15}{-2}$$

Fraction \frac{-15}{-2} can be simplified to \frac{15}{2} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{15}{2}$$