Solve 2+y^2=8

$$2 + y ^ { 2 } = 8$$

Solve for y

$$y=\sqrt{6}\approx 2.449489743$$

$$y=-\sqrt{6}\approx -2.449489743$$

Steps by Finding Square Root

Subtract 2 from both sides.

$$y^{2}=8-2$$

Subtract 2 from 8 to get 6.

$$y^{2}=6$$

Take the square root of both sides of the equation.

$$y=\sqrt{6} y=-\sqrt{6}$$

Steps Using the Quadratic Formula

Subtract 8 from both sides.

$$2+y^{2}-8=0$$

Subtract 8 from 2 to get -6.

$$-6+y^{2}=0$$

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.

$$y^{2}-6=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -6 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{0±\sqrt{0^{2}-4\left(-6\right)}}{2}$$

Square 0.

$$y=\frac{0±\sqrt{-4\left(-6\right)}}{2}$$

Multiply -4 times -6.

$$y=\frac{0±\sqrt{24}}{2}$$

Take the square root of 24.

$$y=\frac{0±2\sqrt{6}}{2}$$

Now solve the equation y=\frac{0±2\sqrt{6}}{2} when ± is plus.

$$y=\sqrt{6}$$

Now solve the equation y=\frac{0±2\sqrt{6}}{2} when ± is minus.

$$y=-\sqrt{6}$$

The equation is now solved.

$$y=\sqrt{6} y=-\sqrt{6}$$