Solve 15-x^2=100-(11-x)^2

$$15 - x ^ { 2 } = 100 - ( 11 - x ) ^ { 2 }$$

Solve for x

$$x = \frac{18}{11} = 1\frac{7}{11} \approx 1.636363636$$

Steps for Solving Linear Equation

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(11-x\right)^{2}.

$$15-x^{2}=100-\left(121-22x+x^{2}\right)$$

To find the opposite of 121-22x+x^{2}, find the opposite of each term.

$$15-x^{2}=100-121+22x-x^{2}$$

Subtract 121 from 100 to get -21.

$$15-x^{2}=-21+22x-x^{2}$$

Subtract 22x from both sides.

$$15-x^{2}-22x=-21-x^{2}$$

Add x^{2} to both sides.

$$15-x^{2}-22x+x^{2}=-21$$

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

$$15-22x=-21$$

Subtract 15 from both sides.

$$-22x=-21-15$$

Subtract 15 from -21 to get -36.

$$-22x=-36$$

Divide both sides by -22.

$$x=\frac{-36}{-22}$$

Reduce the fraction \frac{-36}{-22} to lowest terms by extracting and canceling out -2.

$$x=\frac{18}{11}$$