Solve a^2+5=11

$$a ^ { 2 } + 5 = 11$$

Solve for a

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

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

Steps by Finding Square Root

Subtract 5 from both sides.

$$a^{2}=11-5$$

Subtract 5 from 11 to get 6.

$$a^{2}=6$$

Take the square root of both sides of the equation.

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

Steps Using the Quadratic Formula

Subtract 11 from both sides.

$$a^{2}+5-11=0$$

Subtract 11 from 5 to get -6.

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

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}.

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

Square 0.

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

Multiply -4 times -6.

$$a=\frac{0±\sqrt{24}}{2}$$

Take the square root of 24.

$$a=\frac{0±2\sqrt{6}}{2}$$

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

$$a=\sqrt{6}$$

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

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

The equation is now solved.

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