Solve 6^2+x^2=(34-x)^2-24^2

$$6 ^ { 2 } + x ^ { 2 } = ( 34 - x ) ^ { 2 } - 24 ^ { 2 }$$

Solve for x

$$x=8$$

Steps for Solving Linear Equation

Calculate 6 to the power of 2 and get 36.

$$36+x^{2}=\left(34-x\right)^{2}-24^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(34-x\right)^{2}.

$$36+x^{2}=1156-68x+x^{2}-24^{2}$$

Calculate 24 to the power of 2 and get 576.

$$36+x^{2}=1156-68x+x^{2}-576$$

Subtract 576 from 1156 to get 580.

$$36+x^{2}=580-68x+x^{2}$$

Add 68x to both sides.

$$36+x^{2}+68x=580+x^{2}$$

Subtract x^{2} from both sides.

$$36+x^{2}+68x-x^{2}=580$$

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

$$36+68x=580$$

Subtract 36 from both sides.

$$68x=580-36$$

Subtract 36 from 580 to get 544.

$$68x=544$$

Divide both sides by 68.

$$x=\frac{544}{68}$$

Divide 544 by 68 to get 8.

$$x=8$$