Solve 4x^2-32=0

$$4 x ^ { 2 } - 32 = 0$$

Solve for x

$$x=2\sqrt{2}\approx 2.828427125$$

$$x=-2\sqrt{2}\approx -2.828427125$$

Steps by Finding Square Root

Add 32 to both sides. Anything plus zero gives itself.

$$4x^{2}=32$$

Divide both sides by 4.

$$x^{2}=\frac{32}{4}$$

Divide 32 by 4 to get 8.

$$x^{2}=8$$

Take the square root of both sides of the equation.

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

Steps Using the Quadratic Formula

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$4x^{2}-32=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 4 for a, 0 for b, and -32 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 4\left(-32\right)}}{2\times 4}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 4\left(-32\right)}}{2\times 4}$$

Multiply -4 times 4.

$$x=\frac{0±\sqrt{-16\left(-32\right)}}{2\times 4}$$

Multiply -16 times -32.

$$x=\frac{0±\sqrt{512}}{2\times 4}$$

Take the square root of 512.

$$x=\frac{0±16\sqrt{2}}{2\times 4}$$

Multiply 2 times 4.

$$x=\frac{0±16\sqrt{2}}{8}$$

Now solve the equation x=\frac{0±16\sqrt{2}}{8} when ± is plus.

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

Now solve the equation x=\frac{0±16\sqrt{2}}{8} when ± is minus.

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

The equation is now solved.

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