Solve -y^2=(13)^2+(3-3)^2(5-3)^2/3

$$- y ^ { 2 } = \frac { ( 13 ) ^ { 2 } + ( 3 - 3 ) ^ { 2 } ( 5 - 3 ) ^ { 2 } } { 3 }$$

Solve for y

$$y=-\frac{13\sqrt{3}i}{3}\approx -0-7.505553499i$$

$$y=\frac{13\sqrt{3}i}{3}\approx 7.505553499i$$

Steps by Finding Square Root

Multiply both sides of the equation by 3.

$$-3y^{2}=13^{2}+\left(3-3\right)^{2}\left(5-3\right)^{2}$$

Calculate 13 to the power of 2 and get 169.

$$-3y^{2}=169+\left(3-3\right)^{2}\left(5-3\right)^{2}$$

Subtract 3 from 3 to get 0.

$$-3y^{2}=169+0^{2}\left(5-3\right)^{2}$$

Calculate 0 to the power of 2 and get 0.

$$-3y^{2}=169+0\left(5-3\right)^{2}$$

Subtract 3 from 5 to get 2.

$$-3y^{2}=169+0\times 2^{2}$$

Calculate 2 to the power of 2 and get 4.

$$-3y^{2}=169+0\times 4$$

Multiply 0 and 4 to get 0.

$$-3y^{2}=169+0$$

Add 169 and 0 to get 169.

$$-3y^{2}=169$$

Divide both sides by -3.

$$y^{2}=-\frac{169}{3}$$

The equation is now solved.

$$y=\frac{13\sqrt{3}i}{3} y=-\frac{13\sqrt{3}i}{3}$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 3.

$$-3y^{2}=13^{2}+\left(3-3\right)^{2}\left(5-3\right)^{2}$$

Calculate 13 to the power of 2 and get 169.

$$-3y^{2}=169+\left(3-3\right)^{2}\left(5-3\right)^{2}$$

Subtract 3 from 3 to get 0.

$$-3y^{2}=169+0^{2}\left(5-3\right)^{2}$$

Calculate 0 to the power of 2 and get 0.

$$-3y^{2}=169+0\left(5-3\right)^{2}$$

Subtract 3 from 5 to get 2.

$$-3y^{2}=169+0\times 2^{2}$$

Calculate 2 to the power of 2 and get 4.

$$-3y^{2}=169+0\times 4$$

Multiply 0 and 4 to get 0.

$$-3y^{2}=169+0$$

Add 169 and 0 to get 169.

$$-3y^{2}=169$$

Subtract 169 from both sides.

$$-3y^{2}-169=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -3 for a, 0 for b, and -169 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{0±\sqrt{0^{2}-4\left(-3\right)\left(-169\right)}}{2\left(-3\right)}$$

Square 0.

$$y=\frac{0±\sqrt{-4\left(-3\right)\left(-169\right)}}{2\left(-3\right)}$$

Multiply -4 times -3.

$$y=\frac{0±\sqrt{12\left(-169\right)}}{2\left(-3\right)}$$

Multiply 12 times -169.

$$y=\frac{0±\sqrt{-2028}}{2\left(-3\right)}$$

Take the square root of -2028.

$$y=\frac{0±26\sqrt{3}i}{2\left(-3\right)}$$

Multiply 2 times -3.

$$y=\frac{0±26\sqrt{3}i}{-6}$$

Now solve the equation y=\frac{0±26\sqrt{3}i}{-6} when ± is plus.

$$y=-\frac{13\sqrt{3}i}{3}$$

Now solve the equation y=\frac{0±26\sqrt{3}i}{-6} when ± is minus.

$$y=\frac{13\sqrt{3}i}{3}$$

The equation is now solved.

$$y=-\frac{13\sqrt{3}i}{3} y=\frac{13\sqrt{3}i}{3}$$