Solve y^2-9/25-y^2/36=1

$$\frac { y ^ { 2 } - 9 } { 25 } - \frac { y ^ { 2 } } { 36 } = 1$$

Solve for y

$$y = \frac{6 \sqrt{374}}{11} \approx 10.548588876$$

$$y = -\frac{6 \sqrt{374}}{11} \approx -10.548588876$$

Steps by Finding Square Root

Multiply both sides of the equation by 900, the least common multiple of 25,36.

$$36\left(y^{2}-9\right)-25y^{2}=900$$

Use the distributive property to multiply 36 by y^{2}-9.

$$36y^{2}-324-25y^{2}=900$$

Combine 36y^{2} and -25y^{2} to get 11y^{2}.

$$11y^{2}-324=900$$

Add 324 to both sides.

$$11y^{2}=900+324$$

Add 900 and 324 to get 1224.

$$11y^{2}=1224$$

Divide both sides by 11.

$$y^{2}=\frac{1224}{11}$$

Take the square root of both sides of the equation.

$$y=\frac{6\sqrt{374}}{11} y=-\frac{6\sqrt{374}}{11}$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 900, the least common multiple of 25,36.

$$36\left(y^{2}-9\right)-25y^{2}=900$$

Use the distributive property to multiply 36 by y^{2}-9.

$$36y^{2}-324-25y^{2}=900$$

Combine 36y^{2} and -25y^{2} to get 11y^{2}.

$$11y^{2}-324=900$$

Subtract 900 from both sides.

$$11y^{2}-324-900=0$$

Subtract 900 from -324 to get -1224.

$$11y^{2}-1224=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 11 for a, 0 for b, and -1224 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{0±\sqrt{0^{2}-4\times 11\left(-1224\right)}}{2\times 11}$$

Square 0.

$$y=\frac{0±\sqrt{-4\times 11\left(-1224\right)}}{2\times 11}$$

Multiply -4 times 11.

$$y=\frac{0±\sqrt{-44\left(-1224\right)}}{2\times 11}$$

Multiply -44 times -1224.

$$y=\frac{0±\sqrt{53856}}{2\times 11}$$

Take the square root of 53856.

$$y=\frac{0±12\sqrt{374}}{2\times 11}$$

Multiply 2 times 11.

$$y=\frac{0±12\sqrt{374}}{22}$$

Now solve the equation y=\frac{0±12\sqrt{374}}{22} when ± is plus.

$$y=\frac{6\sqrt{374}}{11}$$

Now solve the equation y=\frac{0±12\sqrt{374}}{22} when ± is minus.

$$y=-\frac{6\sqrt{374}}{11}$$

The equation is now solved.

$$y=\frac{6\sqrt{374}}{11} y=-\frac{6\sqrt{374}}{11}$$