Solve a^2-3=7

$$a ^ { 2 } - 3 = 7$$

Solve for a

$$a=\sqrt{10}\approx 3.16227766$$

$$a=-\sqrt{10}\approx -3.16227766$$

Steps by Finding Square Root

Add 3 to both sides.

$$a^{2}=7+3$$

Add 7 and 3 to get 10.

$$a^{2}=10$$

Take the square root of both sides of the equation.

$$a=\sqrt{10} a=-\sqrt{10}$$

Steps Using the Quadratic Formula

Subtract 7 from both sides.

$$a^{2}-3-7=0$$

Subtract 7 from -3 to get -10.

$$a^{2}-10=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -10 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{0±\sqrt{0^{2}-4\left(-10\right)}}{2}$$

Square 0.

$$a=\frac{0±\sqrt{-4\left(-10\right)}}{2}$$

Multiply -4 times -10.

$$a=\frac{0±\sqrt{40}}{2}$$

Take the square root of 40.

$$a=\frac{0±2\sqrt{10}}{2}$$

Now solve the equation a=\frac{0±2\sqrt{10}}{2} when ± is plus.

$$a=\sqrt{10}$$

Now solve the equation a=\frac{0±2\sqrt{10}}{2} when ± is minus.

$$a=-\sqrt{10}$$

The equation is now solved.

$$a=\sqrt{10} a=-\sqrt{10}$$