Solve 10^2+left(x-2.5right)^2=left(x+2.5right)^2

$${ 10 }^{ 2 } + { \left(x-2.5 \right) }^{ 2 } = { \left(x+2.5 \right) }^{ 2 }$$

Solve for x

$$x=10$$

Steps for Solving Linear Equation

Calculate 10 to the power of 2 and get 100.

$$100+\left(x-2.5\right)^{2}=\left(x+2.5\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-2.5\right)^{2}.

$$100+x^{2}-5x+6.25=\left(x+2.5\right)^{2}$$

Add 100 and 6.25 to get 106.25.

$$106.25+x^{2}-5x=\left(x+2.5\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+2.5\right)^{2}.

$$106.25+x^{2}-5x=x^{2}+5x+6.25$$

Subtract x^{2} from both sides.

$$106.25+x^{2}-5x-x^{2}=5x+6.25$$

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

$$106.25-5x=5x+6.25$$

Subtract 5x from both sides.

$$106.25-5x-5x=6.25$$

Combine -5x and -5x to get -10x.

$$106.25-10x=6.25$$

Subtract 106.25 from both sides.

$$-10x=6.25-106.25$$

Subtract 106.25 from 6.25 to get -100.

$$-10x=-100$$

Divide both sides by -10.

$$x=\frac{-100}{-10}$$

Divide -100 by -10 to get 10.

$$x=10$$