Solve 18^2+y^2=1

$${ 18 }^{ 2 } + { y }^{ 2 } =1$$

Solve for y

$$y=-\sqrt{323}i\approx -0-17.972200756i$$

$$y=\sqrt{323}i\approx 17.972200756i$$

Steps by Finding Square Root

Calculate 18 to the power of 2 and get 324.

$$324+y^{2}=1$$

Subtract 324 from both sides.

$$y^{2}=1-324$$

Subtract 324 from 1 to get -323.

$$y^{2}=-323$$

The equation is now solved.

$$y=\sqrt{323}i y=-\sqrt{323}i$$

Steps Using the Quadratic Formula

Calculate 18 to the power of 2 and get 324.

$$324+y^{2}=1$$

Subtract 1 from both sides.

$$324+y^{2}-1=0$$

Subtract 1 from 324 to get 323.

$$323+y^{2}=0$$

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.

$$y^{2}+323=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 323 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{0±\sqrt{0^{2}-4\times 323}}{2}$$

Square 0.

$$y=\frac{0±\sqrt{-4\times 323}}{2}$$

Multiply -4 times 323.

$$y=\frac{0±\sqrt{-1292}}{2}$$

Take the square root of -1292.

$$y=\frac{0±2\sqrt{323}i}{2}$$

Now solve the equation y=\frac{0±2\sqrt{323}i}{2} when ± is plus.

$$y=\sqrt{323}i$$

Now solve the equation y=\frac{0±2\sqrt{323}i}{2} when ± is minus.

$$y=-\sqrt{323}i$$

The equation is now solved.

$$y=\sqrt{323}i y=-\sqrt{323}i$$