Solve y^2=15^2-12^2

$${ y }^{ 2 } = { 15 }^{ 2 } - { 12 }^{ 2 }$$

Solve for y

$$y=-9$$

$$y=9$$

Steps Using Difference of Squares

Calculate 15 to the power of 2 and get 225.

$$y^{2}=225-12^{2}$$

Calculate 12 to the power of 2 and get 144.

$$y^{2}=225-144$$

Subtract 144 from 225 to get 81.

$$y^{2}=81$$

Subtract 81 from both sides.

$$y^{2}-81=0$$

Consider y^{2}-81. Rewrite y^{2}-81 as y^{2}-9^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(y-9\right)\left(y+9\right)=0$$

To find equation solutions, solve y-9=0 and y+9=0.

$$y=9 y=-9$$

Steps by Finding Square Root

Calculate 15 to the power of 2 and get 225.

$$y^{2}=225-12^{2}$$

Calculate 12 to the power of 2 and get 144.

$$y^{2}=225-144$$

Subtract 144 from 225 to get 81.

$$y^{2}=81$$

Take the square root of both sides of the equation.

$$y=9 y=-9$$

Steps Using the Quadratic Formula

Calculate 15 to the power of 2 and get 225.

$$y^{2}=225-12^{2}$$

Calculate 12 to the power of 2 and get 144.

$$y^{2}=225-144$$

Subtract 144 from 225 to get 81.

$$y^{2}=81$$

Subtract 81 from both sides.

$$y^{2}-81=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -81 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{0±\sqrt{0^{2}-4\left(-81\right)}}{2}$$

Square 0.

$$y=\frac{0±\sqrt{-4\left(-81\right)}}{2}$$

Multiply -4 times -81.

$$y=\frac{0±\sqrt{324}}{2}$$

Take the square root of 324.

$$y=\frac{0±18}{2}$$

Now solve the equation y=\frac{0±18}{2} when ± is plus. Divide 18 by 2.

$$y=9$$

Now solve the equation y=\frac{0±18}{2} when ± is minus. Divide -18 by 2.

$$y=-9$$

The equation is now solved.

$$y=9 y=-9$$