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

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

Solve for y

$$y=-\frac{24\sqrt{61}i}{61}\approx -0-3.072885118i$$

$$y=\frac{24\sqrt{61}i}{61}\approx 3.072885118i$$

Steps by Finding Square Root

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

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

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

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

Combine -36y^{2} and -25y^{2} to get -61y^{2}.

$$324-61y^{2}=900$$

Subtract 324 from both sides.

$$-61y^{2}=900-324$$

Subtract 324 from 900 to get 576.

$$-61y^{2}=576$$

Divide both sides by -61.

$$y^{2}=-\frac{576}{61}$$

The equation is now solved.

$$y=\frac{24\sqrt{61}i}{61} y=-\frac{24\sqrt{61}i}{61}$$

Steps Using the Quadratic Formula

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

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

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

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

Combine -36y^{2} and -25y^{2} to get -61y^{2}.

$$324-61y^{2}=900$$

Subtract 900 from both sides.

$$324-61y^{2}-900=0$$

Subtract 900 from 324 to get -576.

$$-576-61y^{2}=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$-61y^{2}-576=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -61 for a, 0 for b, and -576 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{0±\sqrt{0^{2}-4\left(-61\right)\left(-576\right)}}{2\left(-61\right)}$$

Square 0.

$$y=\frac{0±\sqrt{-4\left(-61\right)\left(-576\right)}}{2\left(-61\right)}$$

Multiply -4 times -61.

$$y=\frac{0±\sqrt{244\left(-576\right)}}{2\left(-61\right)}$$

Multiply 244 times -576.

$$y=\frac{0±\sqrt{-140544}}{2\left(-61\right)}$$

Take the square root of -140544.

$$y=\frac{0±48\sqrt{61}i}{2\left(-61\right)}$$

Multiply 2 times -61.

$$y=\frac{0±48\sqrt{61}i}{-122}$$

Now solve the equation y=\frac{0±48\sqrt{61}i}{-122} when ± is plus.

$$y=-\frac{24\sqrt{61}i}{61}$$

Now solve the equation y=\frac{0±48\sqrt{61}i}{-122} when ± is minus.

$$y=\frac{24\sqrt{61}i}{61}$$

The equation is now solved.

$$y=-\frac{24\sqrt{61}i}{61} y=\frac{24\sqrt{61}i}{61}$$