Solve (8+6x)^2+(8x+6)^2=(10x+10)^2+8

$$( 8 + 6 x ) ^ { 2 } + ( 8 x + 6 ) ^ { 2 } = ( 10 x + 10 ) ^ { 2 } + 8$$

Solve for x

$$x=-1$$

Steps for Solving Linear Equation

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(8+6x\right)^{2}.

$$64+96x+36x^{2}+\left(8x+6\right)^{2}=\left(10x+10\right)^{2}+8$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(8x+6\right)^{2}.

$$64+96x+36x^{2}+64x^{2}+96x+36=\left(10x+10\right)^{2}+8$$

Combine 36x^{2} and 64x^{2} to get 100x^{2}.

$$64+96x+100x^{2}+96x+36=\left(10x+10\right)^{2}+8$$

Combine 96x and 96x to get 192x.

$$64+192x+100x^{2}+36=\left(10x+10\right)^{2}+8$$

Add 64 and 36 to get 100.

$$100+192x+100x^{2}=\left(10x+10\right)^{2}+8$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(10x+10\right)^{2}.

$$100+192x+100x^{2}=100x^{2}+200x+100+8$$

Add 100 and 8 to get 108.

$$100+192x+100x^{2}=100x^{2}+200x+108$$

Subtract 100x^{2} from both sides.

$$100+192x+100x^{2}-100x^{2}=200x+108$$

Combine 100x^{2} and -100x^{2} to get 0.

$$100+192x=200x+108$$

Subtract 200x from both sides.

$$100+192x-200x=108$$

Combine 192x and -200x to get -8x.

$$100-8x=108$$

Subtract 100 from both sides.

$$-8x=108-100$$

Subtract 100 from 108 to get 8.

$$-8x=8$$

Divide both sides by -8.

$$x=\frac{8}{-8}$$

Divide 8 by -8 to get -1.

$$x=-1$$