Solve left(7-xright)^2+25^2=x^2

$${ \left(7-x \right) }^{ 2 } + { 25 }^{ 2 } = { x }^{ 2 }$$

Solve for x

$$x = \frac{337}{7} = 48\frac{1}{7} \approx 48.142857143$$

Steps for Solving Linear Equation

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

$$49-14x+x^{2}+25^{2}=x^{2}$$

Calculate 25 to the power of 2 and get 625.

$$49-14x+x^{2}+625=x^{2}$$

Add 49 and 625 to get 674.

$$674-14x+x^{2}=x^{2}$$

Subtract x^{2} from both sides.

$$674-14x+x^{2}-x^{2}=0$$

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

$$674-14x=0$$

Subtract 674 from both sides. Anything subtracted from zero gives its negation.

$$-14x=-674$$

Divide both sides by -14.

$$x=\frac{-674}{-14}$$

Reduce the fraction \frac{-674}{-14} to lowest terms by extracting and canceling out -2.

$$x=\frac{337}{7}$$