Solve 14^2-y^2=13^2-(15-y)^2

$$14 ^ { 2 } - y ^ { 2 } = 13 ^ { 2 } - ( 15 - y ) ^ { 2 }$$

Solve for y

$$y = \frac{42}{5} = 8\frac{2}{5} = 8.4$$

Steps for Solving Linear Equation

Calculate 14 to the power of 2 and get 196.

$$196-y^{2}=13^{2}-\left(15-y\right)^{2}$$

Calculate 13 to the power of 2 and get 169.

$$196-y^{2}=169-\left(15-y\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(15-y\right)^{2}.

$$196-y^{2}=169-\left(225-30y+y^{2}\right)$$

To find the opposite of 225-30y+y^{2}, find the opposite of each term.

$$196-y^{2}=169-225+30y-y^{2}$$

Subtract 225 from 169 to get -56.

$$196-y^{2}=-56+30y-y^{2}$$

Subtract 30y from both sides.

$$196-y^{2}-30y=-56-y^{2}$$

Add y^{2} to both sides.

$$196-y^{2}-30y+y^{2}=-56$$

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

$$196-30y=-56$$

Subtract 196 from both sides.

$$-30y=-56-196$$

Subtract 196 from -56 to get -252.

$$-30y=-252$$

Divide both sides by -30.

$$y=\frac{-252}{-30}$$

Reduce the fraction \frac{-252}{-30} to lowest terms by extracting and canceling out -6.

$$y=\frac{42}{5}$$