Solve 81v^2-16=0

$$81 v ^ { 2 } - 16 = 0$$

Solve for v

$$v=\frac{4}{9}\approx 0.444444444$$

$$v=-\frac{4}{9}\approx -0.444444444$$

Steps Using Difference of Squares

Consider 81v^{2}-16. Rewrite 81v^{2}-16 as \left(9v\right)^{2}-4^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(9v-4\right)\left(9v+4\right)=0$$

To find equation solutions, solve 9v-4=0 and 9v+4=0.

$$v=\frac{4}{9} v=-\frac{4}{9}$$

Steps by Finding Square Root

Add 16 to both sides. Anything plus zero gives itself.

$$81v^{2}=16$$

Divide both sides by 81.

$$v^{2}=\frac{16}{81}$$

Take the square root of both sides of the equation.

$$v=\frac{4}{9} v=-\frac{4}{9}$$

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.

$$81v^{2}-16=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 81 for a, 0 for b, and -16 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$v=\frac{0±\sqrt{0^{2}-4\times 81\left(-16\right)}}{2\times 81}$$

Square 0.

$$v=\frac{0±\sqrt{-4\times 81\left(-16\right)}}{2\times 81}$$

Multiply -4 times 81.

$$v=\frac{0±\sqrt{-324\left(-16\right)}}{2\times 81}$$

Multiply -324 times -16.

$$v=\frac{0±\sqrt{5184}}{2\times 81}$$

Take the square root of 5184.

$$v=\frac{0±72}{2\times 81}$$

Multiply 2 times 81.

$$v=\frac{0±72}{162}$$

Now solve the equation v=\frac{0±72}{162} when ± is plus. Reduce the fraction \frac{72}{162} to lowest terms by extracting and canceling out 18.

$$v=\frac{4}{9}$$

Now solve the equation v=\frac{0±72}{162} when ± is minus. Reduce the fraction \frac{-72}{162} to lowest terms by extracting and canceling out 18.

$$v=-\frac{4}{9}$$

The equation is now solved.

$$v=\frac{4}{9} v=-\frac{4}{9}$$