Solve 17^2-left(9+xright)^2=10^2-x^2

$${ 17 }^{ 2 } - { \left(9+x \right) }^{ 2 } = { 10 }^{ 2 } - { x }^{ 2 }$$

Solve for x

$$x=6$$

Steps for Solving Linear Equation

Calculate 17 to the power of 2 and get 289.

$$289-\left(9+x\right)^{2}=10^{2}-x^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(9+x\right)^{2}.

$$289-\left(81+18x+x^{2}\right)=10^{2}-x^{2}$$

To find the opposite of 81+18x+x^{2}, find the opposite of each term.

$$289-81-18x-x^{2}=10^{2}-x^{2}$$

Subtract 81 from 289 to get 208.

$$208-18x-x^{2}=10^{2}-x^{2}$$

Calculate 10 to the power of 2 and get 100.

$$208-18x-x^{2}=100-x^{2}$$

Add x^{2} to both sides.

$$208-18x-x^{2}+x^{2}=100$$

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

$$208-18x=100$$

Subtract 208 from both sides.

$$-18x=100-208$$

Subtract 208 from 100 to get -108.

$$-18x=-108$$

Divide both sides by -18.

$$x=\frac{-108}{-18}$$

Divide -108 by -18 to get 6.

$$x=6$$