Solve x^2+2*5^2=(12*5-x)^2

$$x ^ { 2 } + 2 \cdot 5 ^ { 2 } = ( 12 \cdot 5 - x ) ^ { 2 }$$

Solve for x

$$x = \frac{355}{12} = 29\frac{7}{12} \approx 29.583333333$$

Steps for Solving Linear Equation

Calculate 5 to the power of 2 and get 25.

$$x^{2}+2\times 25=\left(12\times 5-x\right)^{2}$$

Multiply 2 and 25 to get 50.

$$x^{2}+50=\left(12\times 5-x\right)^{2}$$

Multiply 12 and 5 to get 60.

$$x^{2}+50=\left(60-x\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(60-x\right)^{2}.

$$x^{2}+50=3600-120x+x^{2}$$

Add 120x to both sides.

$$x^{2}+50+120x=3600+x^{2}$$

Subtract x^{2} from both sides.

$$x^{2}+50+120x-x^{2}=3600$$

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

$$50+120x=3600$$

Subtract 50 from both sides.

$$120x=3600-50$$

Subtract 50 from 3600 to get 3550.

$$120x=3550$$

Divide both sides by 120.

$$x=\frac{3550}{120}$$

Reduce the fraction \frac{3550}{120} to lowest terms by extracting and canceling out 10.

$$x=\frac{355}{12}$$