Solve 64x^2-81=0

$$64 x ^ { 2 } - 81 = 0$$

Solve for x

$$x = \frac{9}{8} = 1\frac{1}{8} = 1.125$$

$$x = -\frac{9}{8} = -1\frac{1}{8} = -1.125$$

Steps Using Difference of Squares

Consider 64x^{2}-81. Rewrite 64x^{2}-81 as \left(8x\right)^{2}-9^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(8x-9\right)\left(8x+9\right)=0$$

To find equation solutions, solve 8x-9=0 and 8x+9=0.

$$x=\frac{9}{8} x=-\frac{9}{8}$$

Steps by Finding Square Root

Add 81 to both sides. Anything plus zero gives itself.

$$64x^{2}=81$$

Divide both sides by 64.

$$x^{2}=\frac{81}{64}$$

Take the square root of both sides of the equation.

$$x=\frac{9}{8} x=-\frac{9}{8}$$

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.

$$64x^{2}-81=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 64 for a, 0 for b, and -81 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 64\left(-81\right)}}{2\times 64}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 64\left(-81\right)}}{2\times 64}$$

Multiply -4 times 64.

$$x=\frac{0±\sqrt{-256\left(-81\right)}}{2\times 64}$$

Multiply -256 times -81.

$$x=\frac{0±\sqrt{20736}}{2\times 64}$$

Take the square root of 20736.

$$x=\frac{0±144}{2\times 64}$$

Multiply 2 times 64.

$$x=\frac{0±144}{128}$$

Now solve the equation x=\frac{0±144}{128} when ± is plus. Reduce the fraction \frac{144}{128} to lowest terms by extracting and canceling out 16.

$$x=\frac{9}{8}$$

Now solve the equation x=\frac{0±144}{128} when ± is minus. Reduce the fraction \frac{-144}{128} to lowest terms by extracting and canceling out 16.

$$x=-\frac{9}{8}$$

The equation is now solved.

$$x=\frac{9}{8} x=-\frac{9}{8}$$