Solve 7^2+left(12-xright)^2=x^2

$${ 7 }^{ 2 } + { \left(12-x \right) }^{ 2 } = { x }^{ 2 }$$

Solve for x

$$x = \frac{193}{24} = 8\frac{1}{24} \approx 8.041666667$$

Steps for Solving Linear Equation

Calculate 7 to the power of 2 and get 49.

$$49+\left(12-x\right)^{2}=x^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(12-x\right)^{2}.

$$49+144-24x+x^{2}=x^{2}$$

Add 49 and 144 to get 193.

$$193-24x+x^{2}=x^{2}$$

Subtract x^{2} from both sides.

$$193-24x+x^{2}-x^{2}=0$$

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

$$193-24x=0$$

Subtract 193 from both sides. Anything subtracted from zero gives its negation.

$$-24x=-193$$

Divide both sides by -24.

$$x=\frac{-193}{-24}$$

Fraction \frac{-193}{-24} can be simplified to \frac{193}{24} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{193}{24}$$