Solve 2^2+y^2=18

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

Solve for y

$$y=\sqrt{14}\approx 3.741657387$$

$$y=-\sqrt{14}\approx -3.741657387$$

Steps by Finding Square Root

Calculate 2 to the power of 2 and get 4.

$$4+y^{2}=18$$

Subtract 4 from both sides.

$$y^{2}=18-4$$

Subtract 4 from 18 to get 14.

$$y^{2}=14$$

Take the square root of both sides of the equation.

$$y=\sqrt{14} y=-\sqrt{14}$$

Steps Using the Quadratic Formula

Calculate 2 to the power of 2 and get 4.

$$4+y^{2}=18$$

Subtract 18 from both sides.

$$4+y^{2}-18=0$$

Subtract 18 from 4 to get -14.

$$-14+y^{2}=0$$

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.

$$y^{2}-14=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -14 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{0±\sqrt{0^{2}-4\left(-14\right)}}{2}$$

Square 0.

$$y=\frac{0±\sqrt{-4\left(-14\right)}}{2}$$

Multiply -4 times -14.

$$y=\frac{0±\sqrt{56}}{2}$$

Take the square root of 56.

$$y=\frac{0±2\sqrt{14}}{2}$$

Now solve the equation y=\frac{0±2\sqrt{14}}{2} when ± is plus.

$$y=\sqrt{14}$$

Now solve the equation y=\frac{0±2\sqrt{14}}{2} when ± is minus.

$$y=-\sqrt{14}$$

The equation is now solved.

$$y=\sqrt{14} y=-\sqrt{14}$$