Solve y^2-2=142

$$y ^ { 2 } - 2 = 142$$

Solve for y

$$y=12$$

$$y=-12$$

Steps Using Difference of Squares

Subtract 142 from both sides.

$$y^{2}-2-142=0$$

Subtract 142 from -2 to get -144.

$$y^{2}-144=0$$

Consider y^{2}-144. Rewrite y^{2}-144 as y^{2}-12^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(y-12\right)\left(y+12\right)=0$$

To find equation solutions, solve y-12=0 and y+12=0.

$$y=12 y=-12$$

Steps by Finding Square Root

Add 2 to both sides.

$$y^{2}=142+2$$

Add 142 and 2 to get 144.

$$y^{2}=144$$

Take the square root of both sides of the equation.

$$y=12 y=-12$$

Steps Using the Quadratic Formula

Subtract 142 from both sides.

$$y^{2}-2-142=0$$

Subtract 142 from -2 to get -144.

$$y^{2}-144=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -144 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{0±\sqrt{0^{2}-4\left(-144\right)}}{2}$$

Square 0.

$$y=\frac{0±\sqrt{-4\left(-144\right)}}{2}$$

Multiply -4 times -144.

$$y=\frac{0±\sqrt{576}}{2}$$

Take the square root of 576.

$$y=\frac{0±24}{2}$$

Now solve the equation y=\frac{0±24}{2} when ± is plus. Divide 24 by 2.

$$y=12$$

Now solve the equation y=\frac{0±24}{2} when ± is minus. Divide -24 by 2.

$$y=-12$$

The equation is now solved.

$$y=12 y=-12$$