Solve 4x^2-2=16

$$4 x ^ { 2 } - 2 = 16$$

Solve for x

$$x = \frac{3 \sqrt{2}}{2} \approx 2.121320344$$

$$x = -\frac{3 \sqrt{2}}{2} \approx -2.121320344$$

Steps by Finding Square Root

Add 2 to both sides.

$$4x^{2}=16+2$$

Add 16 and 2 to get 18.

$$4x^{2}=18$$

Divide both sides by 4.

$$x^{2}=\frac{18}{4}$$

Reduce the fraction \frac{18}{4} to lowest terms by extracting and canceling out 2.

$$x^{2}=\frac{9}{2}$$

Take the square root of both sides of the equation.

$$x=\frac{3\sqrt{2}}{2} x=-\frac{3\sqrt{2}}{2}$$

Steps Using the Quadratic Formula

Subtract 16 from both sides.

$$4x^{2}-2-16=0$$

Subtract 16 from -2 to get -18.

$$4x^{2}-18=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 4 for a, 0 for b, and -18 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 4\left(-18\right)}}{2\times 4}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 4\left(-18\right)}}{2\times 4}$$

Multiply -4 times 4.

$$x=\frac{0±\sqrt{-16\left(-18\right)}}{2\times 4}$$

Multiply -16 times -18.

$$x=\frac{0±\sqrt{288}}{2\times 4}$$

Take the square root of 288.

$$x=\frac{0±12\sqrt{2}}{2\times 4}$$

Multiply 2 times 4.

$$x=\frac{0±12\sqrt{2}}{8}$$

Now solve the equation x=\frac{0±12\sqrt{2}}{8} when ± is plus.

$$x=\frac{3\sqrt{2}}{2}$$

Now solve the equation x=\frac{0±12\sqrt{2}}{8} when ± is minus.

$$x=-\frac{3\sqrt{2}}{2}$$

The equation is now solved.

$$x=\frac{3\sqrt{2}}{2} x=-\frac{3\sqrt{2}}{2}$$