Solve 32x^2-7=0

$$32 x ^ { 2 } - 7 = 0$$

Solve for x

$$x=\frac{\sqrt{14}}{8}\approx 0.467707173$$

$$x=-\frac{\sqrt{14}}{8}\approx -0.467707173$$

Steps by Finding Square Root

Add 7 to both sides. Anything plus zero gives itself.

$$32x^{2}=7$$

Divide both sides by 32.

$$x^{2}=\frac{7}{32}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{14}}{8} x=-\frac{\sqrt{14}}{8}$$

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.

$$32x^{2}-7=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 32 for a, 0 for b, and -7 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 32\left(-7\right)}}{2\times 32}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 32\left(-7\right)}}{2\times 32}$$

Multiply -4 times 32.

$$x=\frac{0±\sqrt{-128\left(-7\right)}}{2\times 32}$$

Multiply -128 times -7.

$$x=\frac{0±\sqrt{896}}{2\times 32}$$

Take the square root of 896.

$$x=\frac{0±8\sqrt{14}}{2\times 32}$$

Multiply 2 times 32.

$$x=\frac{0±8\sqrt{14}}{64}$$

Now solve the equation x=\frac{0±8\sqrt{14}}{64} when ± is plus.

$$x=\frac{\sqrt{14}}{8}$$

Now solve the equation x=\frac{0±8\sqrt{14}}{64} when ± is minus.

$$x=-\frac{\sqrt{14}}{8}$$

The equation is now solved.

$$x=\frac{\sqrt{14}}{8} x=-\frac{\sqrt{14}}{8}$$