Solve 9/9+y^2=9/25

$$\frac { 9 } { 9 + y ^ { 2 } } = \frac { 9 } { 25 }$$

Solve for y

$$y=4$$

$$y=-4$$

Steps Using Difference of Squares

Multiply both sides of the equation by 25\left(y^{2}+9\right), the least common multiple of 9+y^{2},25.

$$25\times 9=9\left(y^{2}+9\right)$$

Multiply 25 and 9 to get 225.

$$225=9\left(y^{2}+9\right)$$

Use the distributive property to multiply 9 by y^{2}+9.

$$225=9y^{2}+81$$

Swap sides so that all variable terms are on the left hand side.

$$9y^{2}+81=225$$

Subtract 225 from both sides.

$$9y^{2}+81-225=0$$

Subtract 225 from 81 to get -144.

$$9y^{2}-144=0$$

Divide both sides by 9.

$$y^{2}-16=0$$

Consider y^{2}-16. Rewrite y^{2}-16 as y^{2}-4^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(y-4\right)\left(y+4\right)=0$$

To find equation solutions, solve y-4=0 and y+4=0.

$$y=4 y=-4$$

Steps by Finding Square Root

Multiply both sides of the equation by 25\left(y^{2}+9\right), the least common multiple of 9+y^{2},25.

$$25\times 9=9\left(y^{2}+9\right)$$

Multiply 25 and 9 to get 225.

$$225=9\left(y^{2}+9\right)$$

Use the distributive property to multiply 9 by y^{2}+9.

$$225=9y^{2}+81$$

Swap sides so that all variable terms are on the left hand side.

$$9y^{2}+81=225$$

Subtract 81 from both sides.

$$9y^{2}=225-81$$

Subtract 81 from 225 to get 144.

$$9y^{2}=144$$

Divide both sides by 9.

$$y^{2}=\frac{144}{9}$$

Divide 144 by 9 to get 16.

$$y^{2}=16$$

Take the square root of both sides of the equation.

$$y=4 y=-4$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 25\left(y^{2}+9\right), the least common multiple of 9+y^{2},25.

$$25\times 9=9\left(y^{2}+9\right)$$

Multiply 25 and 9 to get 225.

$$225=9\left(y^{2}+9\right)$$

Use the distributive property to multiply 9 by y^{2}+9.

$$225=9y^{2}+81$$

Swap sides so that all variable terms are on the left hand side.

$$9y^{2}+81=225$$

Subtract 225 from both sides.

$$9y^{2}+81-225=0$$

Subtract 225 from 81 to get -144.

$$9y^{2}-144=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 9 for a, 0 for b, and -144 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{0±\sqrt{0^{2}-4\times 9\left(-144\right)}}{2\times 9}$$

Square 0.

$$y=\frac{0±\sqrt{-4\times 9\left(-144\right)}}{2\times 9}$$

Multiply -4 times 9.

$$y=\frac{0±\sqrt{-36\left(-144\right)}}{2\times 9}$$

Multiply -36 times -144.

$$y=\frac{0±\sqrt{5184}}{2\times 9}$$

Take the square root of 5184.

$$y=\frac{0±72}{2\times 9}$$

Multiply 2 times 9.

$$y=\frac{0±72}{18}$$

Now solve the equation y=\frac{0±72}{18} when ± is plus. Divide 72 by 18.

$$y=4$$

Now solve the equation y=\frac{0±72}{18} when ± is minus. Divide -72 by 18.

$$y=-4$$

The equation is now solved.

$$y=4 y=-4$$