Solve 6^2+(13-x)^2=x^2

$$6 ^ { 2 } + ( 13 - x ) ^ { 2 } = x ^ { 2 }$$

Solve for x

$$x = \frac{205}{26} = 7\frac{23}{26} \approx 7.884615385$$

Steps for Solving Linear Equation

Calculate 6 to the power of 2 and get 36.

$$36+\left(13-x\right)^{2}=x^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(13-x\right)^{2}.

$$36+169-26x+x^{2}=x^{2}$$

Add 36 and 169 to get 205.

$$205-26x+x^{2}=x^{2}$$

Subtract x^{2} from both sides.

$$205-26x+x^{2}-x^{2}=0$$

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

$$205-26x=0$$

Subtract 205 from both sides. Anything subtracted from zero gives its negation.

$$-26x=-205$$

Divide both sides by -26.

$$x=\frac{-205}{-26}$$

Fraction \frac{-205}{-26} can be simplified to \frac{205}{26} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{205}{26}$$