Solve left(x+6right)^2=left(64+xright)^2+100

$${ \left(x+6 \right) }^{ 2 } = { \left(64+x \right) }^{ 2 } +100$$

Solve for x

$$x = -\frac{1040}{29} = -35\frac{25}{29} \approx -35.862068966$$

Steps for Solving Linear Equation

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+6\right)^{2}.

$$x^{2}+12x+36=\left(64+x\right)^{2}+100$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(64+x\right)^{2}.

$$x^{2}+12x+36=4096+128x+x^{2}+100$$

Add 4096 and 100 to get 4196.

$$x^{2}+12x+36=4196+128x+x^{2}$$

Subtract 128x from both sides.

$$x^{2}+12x+36-128x=4196+x^{2}$$

Combine 12x and -128x to get -116x.

$$x^{2}-116x+36=4196+x^{2}$$

Subtract x^{2} from both sides.

$$x^{2}-116x+36-x^{2}=4196$$

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

$$-116x+36=4196$$

Subtract 36 from both sides.

$$-116x=4196-36$$

Subtract 36 from 4196 to get 4160.

$$-116x=4160$$

Divide both sides by -116.

$$x=\frac{4160}{-116}$$

Reduce the fraction \frac{4160}{-116} to lowest terms by extracting and canceling out 4.

$$x=-\frac{1040}{29}$$