Solve 4^2/4+y^2/9=1

$$\frac{ { 4 }^{ 2 } }{ 4 } + \frac{ { y }^{ 2 } }{ 9 } = 1$$

Solve for y

$$y=-3\sqrt{3}i\approx -0-5.196152423i$$

$$y=3\sqrt{3}i\approx 5.196152423i$$

Steps by Finding Square Root

Multiply both sides of the equation by 36, the least common multiple of 4,9.

$$9\times 4^{2}+4y^{2}=36$$

Calculate 4 to the power of 2 and get 16.

$$9\times 16+4y^{2}=36$$

Multiply 9 and 16 to get 144.

$$144+4y^{2}=36$$

Subtract 144 from both sides.

$$4y^{2}=36-144$$

Subtract 144 from 36 to get -108.

$$4y^{2}=-108$$

Divide both sides by 4.

$$y^{2}=\frac{-108}{4}$$

Divide -108 by 4 to get -27.

$$y^{2}=-27$$

The equation is now solved.

$$y=3\sqrt{3}i y=-3\sqrt{3}i$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 36, the least common multiple of 4,9.

$$9\times 4^{2}+4y^{2}=36$$

Calculate 4 to the power of 2 and get 16.

$$9\times 16+4y^{2}=36$$

Multiply 9 and 16 to get 144.

$$144+4y^{2}=36$$

Subtract 36 from both sides.

$$144+4y^{2}-36=0$$

Subtract 36 from 144 to get 108.

$$108+4y^{2}=0$$

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.

$$4y^{2}+108=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 4 for a, 0 for b, and 108 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{0±\sqrt{0^{2}-4\times 4\times 108}}{2\times 4}$$

Square 0.

$$y=\frac{0±\sqrt{-4\times 4\times 108}}{2\times 4}$$

Multiply -4 times 4.

$$y=\frac{0±\sqrt{-16\times 108}}{2\times 4}$$

Multiply -16 times 108.

$$y=\frac{0±\sqrt{-1728}}{2\times 4}$$

Take the square root of -1728.

$$y=\frac{0±24\sqrt{3}i}{2\times 4}$$

Multiply 2 times 4.

$$y=\frac{0±24\sqrt{3}i}{8}$$

Now solve the equation y=\frac{0±24\sqrt{3}i}{8} when ± is plus.

$$y=3\sqrt{3}i$$

Now solve the equation y=\frac{0±24\sqrt{3}i}{8} when ± is minus.

$$y=-3\sqrt{3}i$$

The equation is now solved.

$$y=3\sqrt{3}i y=-3\sqrt{3}i$$