Solve 100=4x^2-22

$$100=4 { x }^{ 2 } -22$$

Solve for x

$$x = \frac{\sqrt{122}}{2} \approx 5.522680509$$

$$x = -\frac{\sqrt{122}}{2} \approx -5.522680509$$

Steps by Finding Square Root

Swap sides so that all variable terms are on the left hand side.

$$4x^{2}-22=100$$

Add 22 to both sides.

$$4x^{2}=100+22$$

Add 100 and 22 to get 122.

$$4x^{2}=122$$

Divide both sides by 4.

$$x^{2}=\frac{122}{4}$$

Reduce the fraction \frac{122}{4} to lowest terms by extracting and canceling out 2.

$$x^{2}=\frac{61}{2}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{122}}{2} x=-\frac{\sqrt{122}}{2}$$

Steps Using the Quadratic Formula

Swap sides so that all variable terms are on the left hand side.

$$4x^{2}-22=100$$

Subtract 100 from both sides.

$$4x^{2}-22-100=0$$

Subtract 100 from -22 to get -122.

$$4x^{2}-122=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 4 for a, 0 for b, and -122 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 4\left(-122\right)}}{2\times 4}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 4\left(-122\right)}}{2\times 4}$$

Multiply -4 times 4.

$$x=\frac{0±\sqrt{-16\left(-122\right)}}{2\times 4}$$

Multiply -16 times -122.

$$x=\frac{0±\sqrt{1952}}{2\times 4}$$

Take the square root of 1952.

$$x=\frac{0±4\sqrt{122}}{2\times 4}$$

Multiply 2 times 4.

$$x=\frac{0±4\sqrt{122}}{8}$$

Now solve the equation x=\frac{0±4\sqrt{122}}{8} when ± is plus.

$$x=\frac{\sqrt{122}}{2}$$

Now solve the equation x=\frac{0±4\sqrt{122}}{8} when ± is minus.

$$x=-\frac{\sqrt{122}}{2}$$

The equation is now solved.

$$x=\frac{\sqrt{122}}{2} x=-\frac{\sqrt{122}}{2}$$