Solve 10^2-x^2=17^2-(9-x)^2

$$10 ^ { 2 } - x ^ { 2 } = 17 ^ { 2 } - ( 9 - x ) ^ { 2 }$$

Solve for x

$$x=-6$$

Steps for Solving Linear Equation

Calculate 10 to the power of 2 and get 100.

$$100-x^{2}=17^{2}-\left(9-x\right)^{2}$$

Calculate 17 to the power of 2 and get 289.

$$100-x^{2}=289-\left(9-x\right)^{2}$$

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

$$100-x^{2}=289-\left(81-18x+x^{2}\right)$$

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

$$100-x^{2}=289-81+18x-x^{2}$$

Subtract 81 from 289 to get 208.

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

Subtract 18x from both sides.

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

Add x^{2} to both sides.

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

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

$$100-18x=208$$

Subtract 100 from both sides.

$$-18x=208-100$$

Subtract 100 from 208 to get 108.

$$-18x=108$$

Divide both sides by -18.

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

Divide 108 by -18 to get -6.

$$x=-6$$