Solve 64x^2=9

$$64 x ^ { 2 } = 9$$

Solve for x

$$x=\frac{3}{8}=0.375$$

$$x=-\frac{3}{8}=-0.375$$

Steps Using Difference of Squares

Divide both sides by 64.

$$x^{2}=\frac{9}{64}$$

Subtract \frac{9}{64} from both sides.

$$x^{2}-\frac{9}{64}=0$$

Multiply both sides by 64.

$$64x^{2}-9=0$$

Consider 64x^{2}-9. Rewrite 64x^{2}-9 as \left(8x\right)^{2}-3^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(8x-3\right)\left(8x+3\right)=0$$

To find equation solutions, solve 8x-3=0 and 8x+3=0.

$$x=\frac{3}{8} x=-\frac{3}{8}$$

Steps by Finding Square Root

Divide both sides by 64.

$$x^{2}=\frac{9}{64}$$

Take the square root of both sides of the equation.

$$x=\frac{3}{8} x=-\frac{3}{8}$$

Steps Using the Quadratic Formula

Divide both sides by 64.

$$x^{2}=\frac{9}{64}$$

Subtract \frac{9}{64} from both sides.

$$x^{2}-\frac{9}{64}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{9}{64} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{9}{64}\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{9}{64}\right)}}{2}$$

Multiply -4 times -\frac{9}{64}.

$$x=\frac{0±\sqrt{\frac{9}{16}}}{2}$$

Take the square root of \frac{9}{16}.

$$x=\frac{0±\frac{3}{4}}{2}$$

Now solve the equation x=\frac{0±\frac{3}{4}}{2} when ± is plus.

$$x=\frac{3}{8}$$

Now solve the equation x=\frac{0±\frac{3}{4}}{2} when ± is minus.

$$x=-\frac{3}{8}$$

The equation is now solved.

$$x=\frac{3}{8} x=-\frac{3}{8}$$