Solve x^2-7=33

$$x ^ { 2 } - 7 = 33$$

Solve for x

$$x=2\sqrt{10}\approx 6.32455532$$

$$x=-2\sqrt{10}\approx -6.32455532$$

Steps by Finding Square Root

Add 7 to both sides.

$$x^{2}=33+7$$

Add 33 and 7 to get 40.

$$x^{2}=40$$

Take the square root of both sides of the equation.

$$x=2\sqrt{10} x=-2\sqrt{10}$$

Steps Using the Quadratic Formula

Subtract 33 from both sides.

$$x^{2}-7-33=0$$

Subtract 33 from -7 to get -40.

$$x^{2}-40=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -40 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-40\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-40\right)}}{2}$$

Multiply -4 times -40.

$$x=\frac{0±\sqrt{160}}{2}$$

Take the square root of 160.

$$x=\frac{0±4\sqrt{10}}{2}$$

Now solve the equation x=\frac{0±4\sqrt{10}}{2} when ± is plus.

$$x=2\sqrt{10}$$

Now solve the equation x=\frac{0±4\sqrt{10}}{2} when ± is minus.

$$x=-2\sqrt{10}$$

The equation is now solved.

$$x=2\sqrt{10} x=-2\sqrt{10}$$