Solve 640x^2-36=0

$$640 x ^ { 2 } - 36 = 0$$

Solve for x

$$x=\frac{3\sqrt{10}}{40}\approx 0.237170825$$

$$x=-\frac{3\sqrt{10}}{40}\approx -0.237170825$$

Steps by Finding Square Root

Add 36 to both sides. Anything plus zero gives itself.

$$640x^{2}=36$$

Divide both sides by 640.

$$x^{2}=\frac{36}{640}$$

Reduce the fraction \frac{36}{640} to lowest terms by extracting and canceling out 4.

$$x^{2}=\frac{9}{160}$$

Take the square root of both sides of the equation.

$$x=\frac{3\sqrt{10}}{40} x=-\frac{3\sqrt{10}}{40}$$

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.

$$640x^{2}-36=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 640 for a, 0 for b, and -36 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 640\left(-36\right)}}{2\times 640}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 640\left(-36\right)}}{2\times 640}$$

Multiply -4 times 640.

$$x=\frac{0±\sqrt{-2560\left(-36\right)}}{2\times 640}$$

Multiply -2560 times -36.

$$x=\frac{0±\sqrt{92160}}{2\times 640}$$

Take the square root of 92160.

$$x=\frac{0±96\sqrt{10}}{2\times 640}$$

Multiply 2 times 640.

$$x=\frac{0±96\sqrt{10}}{1280}$$

Now solve the equation x=\frac{0±96\sqrt{10}}{1280} when ± is plus.

$$x=\frac{3\sqrt{10}}{40}$$

Now solve the equation x=\frac{0±96\sqrt{10}}{1280} when ± is minus.

$$x=-\frac{3\sqrt{10}}{40}$$

The equation is now solved.

$$x=\frac{3\sqrt{10}}{40} x=-\frac{3\sqrt{10}}{40}$$