Solve 81y^2-36=0

$$81 y ^ { 2 } - 36 = 0$$

Solve for y

$$y=\frac{2}{3}\approx 0.666666667$$

$$y=-\frac{2}{3}\approx -0.666666667$$

Steps Using Difference of Squares

Divide both sides by 9.

$$9y^{2}-4=0$$

Consider 9y^{2}-4. Rewrite 9y^{2}-4 as \left(3y\right)^{2}-2^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(3y-2\right)\left(3y+2\right)=0$$

To find equation solutions, solve 3y-2=0 and 3y+2=0.

$$y=\frac{2}{3} y=-\frac{2}{3}$$

Steps by Finding Square Root

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

$$81y^{2}=36$$

Divide both sides by 81.

$$y^{2}=\frac{36}{81}$$

Reduce the fraction \frac{36}{81} to lowest terms by extracting and canceling out 9.

$$y^{2}=\frac{4}{9}$$

Take the square root of both sides of the equation.

$$y=\frac{2}{3} y=-\frac{2}{3}$$

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.

$$81y^{2}-36=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 81 for a, 0 for b, and -36 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{0±\sqrt{0^{2}-4\times 81\left(-36\right)}}{2\times 81}$$

Square 0.

$$y=\frac{0±\sqrt{-4\times 81\left(-36\right)}}{2\times 81}$$

Multiply -4 times 81.

$$y=\frac{0±\sqrt{-324\left(-36\right)}}{2\times 81}$$

Multiply -324 times -36.

$$y=\frac{0±\sqrt{11664}}{2\times 81}$$

Take the square root of 11664.

$$y=\frac{0±108}{2\times 81}$$

Multiply 2 times 81.

$$y=\frac{0±108}{162}$$

Now solve the equation y=\frac{0±108}{162} when ± is plus. Reduce the fraction \frac{108}{162} to lowest terms by extracting and canceling out 54.

$$y=\frac{2}{3}$$

Now solve the equation y=\frac{0±108}{162} when ± is minus. Reduce the fraction \frac{-108}{162} to lowest terms by extracting and canceling out 54.

$$y=-\frac{2}{3}$$

The equation is now solved.

$$y=\frac{2}{3} y=-\frac{2}{3}$$