Solve 64y^2=81

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

Solve for y

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

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

Steps Using Difference of Squares

Divide both sides by 64.

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

Subtract \frac{81}{64} from both sides.

$$y^{2}-\frac{81}{64}=0$$

Multiply both sides by 64.

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

Consider 64y^{2}-81. Rewrite 64y^{2}-81 as \left(8y\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).

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

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

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

Steps by Finding Square Root

Divide both sides by 64.

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

Take the square root of both sides of the equation.

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

Steps Using the Quadratic Formula

Divide both sides by 64.

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

Subtract \frac{81}{64} from both sides.

$$y^{2}-\frac{81}{64}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{81}{64} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

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

Square 0.

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

Multiply -4 times -\frac{81}{64}.

$$y=\frac{0±\sqrt{\frac{81}{16}}}{2}$$

Take the square root of \frac{81}{16}.

$$y=\frac{0±\frac{9}{4}}{2}$$

Now solve the equation y=\frac{0±\frac{9}{4}}{2} when ± is plus.

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

Now solve the equation y=\frac{0±\frac{9}{4}}{2} when ± is minus.

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

The equation is now solved.

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