Solve varepsilon^2-2=9

$$\varepsilon ^ { 2 } - 2 = 9$$

Solve for ε

$$\epsilon =\sqrt{11}\approx 3.31662479$$

$$\epsilon =-\sqrt{11}\approx -3.31662479$$

Steps by Finding Square Root

Add 2 to both sides.

$$\epsilon ^{2}=9+2$$

Add 9 and 2 to get 11.

$$\epsilon ^{2}=11$$

Take the square root of both sides of the equation.

$$\epsilon =\sqrt{11} \epsilon =-\sqrt{11}$$

Steps Using the Quadratic Formula

Subtract 9 from both sides.

$$\epsilon ^{2}-2-9=0$$

Subtract 9 from -2 to get -11.

$$\epsilon ^{2}-11=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -11 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$\epsilon =\frac{0±\sqrt{0^{2}-4\left(-11\right)}}{2}$$

Square 0.

$$\epsilon =\frac{0±\sqrt{-4\left(-11\right)}}{2}$$

Multiply -4 times -11.

$$\epsilon =\frac{0±\sqrt{44}}{2}$$

Take the square root of 44.

$$\epsilon =\frac{0±2\sqrt{11}}{2}$$

Now solve the equation \epsilon =\frac{0±2\sqrt{11}}{2} when ± is plus.

$$\epsilon =\sqrt{11}$$

Now solve the equation \epsilon =\frac{0±2\sqrt{11}}{2} when ± is minus.

$$\epsilon =-\sqrt{11}$$

The equation is now solved.

$$\epsilon =\sqrt{11} \epsilon =-\sqrt{11}$$