Solve (4y/16)^2+y^2=150^2

$$( \frac { 4 y } { 16 } ) ^ { 2 } + y ^ { 2 } = 150 ^ { 2 }$$

Solve for y

$$y = \frac{600 \sqrt{17}}{17} \approx 145.521375022$$

$$y = -\frac{600 \sqrt{17}}{17} \approx -145.521375022$$

Steps by Finding Square Root

Divide 4y by 16 to get \frac{1}{4}y.

$$\left(\frac{1}{4}y\right)^{2}+y^{2}=150^{2}$$

Expand \left(\frac{1}{4}y\right)^{2}.

$$\left(\frac{1}{4}\right)^{2}y^{2}+y^{2}=150^{2}$$

Calculate \frac{1}{4} to the power of 2 and get \frac{1}{16}.

$$\frac{1}{16}y^{2}+y^{2}=150^{2}$$

Combine \frac{1}{16}y^{2} and y^{2} to get \frac{17}{16}y^{2}.

$$\frac{17}{16}y^{2}=150^{2}$$

Calculate 150 to the power of 2 and get 22500.

$$\frac{17}{16}y^{2}=22500$$

Multiply both sides by \frac{16}{17}, the reciprocal of \frac{17}{16}.

$$y^{2}=22500\times \frac{16}{17}$$

Multiply 22500 and \frac{16}{17} to get \frac{360000}{17}.

$$y^{2}=\frac{360000}{17}$$

Take the square root of both sides of the equation.

$$y=\frac{600\sqrt{17}}{17} y=-\frac{600\sqrt{17}}{17}$$

Steps Using the Quadratic Formula

Divide 4y by 16 to get \frac{1}{4}y.

$$\left(\frac{1}{4}y\right)^{2}+y^{2}=150^{2}$$

Expand \left(\frac{1}{4}y\right)^{2}.

$$\left(\frac{1}{4}\right)^{2}y^{2}+y^{2}=150^{2}$$

Calculate \frac{1}{4} to the power of 2 and get \frac{1}{16}.

$$\frac{1}{16}y^{2}+y^{2}=150^{2}$$

Combine \frac{1}{16}y^{2} and y^{2} to get \frac{17}{16}y^{2}.

$$\frac{17}{16}y^{2}=150^{2}$$

Calculate 150 to the power of 2 and get 22500.

$$\frac{17}{16}y^{2}=22500$$

Subtract 22500 from both sides.

$$\frac{17}{16}y^{2}-22500=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{17}{16} for a, 0 for b, and -22500 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{0±\sqrt{0^{2}-4\times \frac{17}{16}\left(-22500\right)}}{2\times \frac{17}{16}}$$

Square 0.

$$y=\frac{0±\sqrt{-4\times \frac{17}{16}\left(-22500\right)}}{2\times \frac{17}{16}}$$

Multiply -4 times \frac{17}{16}.

$$y=\frac{0±\sqrt{-\frac{17}{4}\left(-22500\right)}}{2\times \frac{17}{16}}$$

Multiply -\frac{17}{4} times -22500.

$$y=\frac{0±\sqrt{95625}}{2\times \frac{17}{16}}$$

Take the square root of 95625.

$$y=\frac{0±75\sqrt{17}}{2\times \frac{17}{16}}$$

Multiply 2 times \frac{17}{16}.

$$y=\frac{0±75\sqrt{17}}{\frac{17}{8}}$$

Now solve the equation y=\frac{0±75\sqrt{17}}{\frac{17}{8}} when ± is plus.

$$y=\frac{600\sqrt{17}}{17}$$

Now solve the equation y=\frac{0±75\sqrt{17}}{\frac{17}{8}} when ± is minus.

$$y=-\frac{600\sqrt{17}}{17}$$

The equation is now solved.

$$y=\frac{600\sqrt{17}}{17} y=-\frac{600\sqrt{17}}{17}$$