Solve 64x^2-9=0

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

Solve for x

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

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

Steps Using Difference of Squares

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

Add 9 to both sides. Anything plus zero gives itself.

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

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

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.

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

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

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

Square 0.

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

Multiply -4 times 64.

$$x=\frac{0±\sqrt{-256\left(-9\right)}}{2\times 64}$$

Multiply -256 times -9.

$$x=\frac{0±\sqrt{2304}}{2\times 64}$$

Take the square root of 2304.

$$x=\frac{0±48}{2\times 64}$$

Multiply 2 times 64.

$$x=\frac{0±48}{128}$$

Now solve the equation x=\frac{0±48}{128} when ± is plus. Reduce the fraction \frac{48}{128} to lowest terms by extracting and canceling out 16.

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

Now solve the equation x=\frac{0±48}{128} when ± is minus. Reduce the fraction \frac{-48}{128} to lowest terms by extracting and canceling out 16.

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

The equation is now solved.

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