Solve 9x^2=16

$$9 { x }^{ 2 } =16$$

Solve for x

$$x = \frac{4}{3} = 1\frac{1}{3} \approx 1.333333333$$

$$x = -\frac{4}{3} = -1\frac{1}{3} \approx -1.333333333$$

Steps Using Difference of Squares

Divide both sides by 9.

$$x^{2}=\frac{16}{9}$$

Subtract \frac{16}{9} from both sides.

$$x^{2}-\frac{16}{9}=0$$

Multiply both sides by 9.

$$9x^{2}-16=0$$

Consider 9x^{2}-16. Rewrite 9x^{2}-16 as \left(3x\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).

$$\left(3x-4\right)\left(3x+4\right)=0$$

To find equation solutions, solve 3x-4=0 and 3x+4=0.

$$x=\frac{4}{3} x=-\frac{4}{3}$$

Steps by Finding Square Root

Divide both sides by 9.

$$x^{2}=\frac{16}{9}$$

Take the square root of both sides of the equation.

$$x=\frac{4}{3} x=-\frac{4}{3}$$

Steps Using the Quadratic Formula

Divide both sides by 9.

$$x^{2}=\frac{16}{9}$$

Subtract \frac{16}{9} from both sides.

$$x^{2}-\frac{16}{9}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{16}{9} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{16}{9}\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{16}{9}\right)}}{2}$$

Multiply -4 times -\frac{16}{9}.

$$x=\frac{0±\sqrt{\frac{64}{9}}}{2}$$

Take the square root of \frac{64}{9}.

$$x=\frac{0±\frac{8}{3}}{2}$$

Now solve the equation x=\frac{0±\frac{8}{3}}{2} when ± is plus.

$$x=\frac{4}{3}$$

Now solve the equation x=\frac{0±\frac{8}{3}}{2} when ± is minus.

$$x=-\frac{4}{3}$$

The equation is now solved.

$$x=\frac{4}{3} x=-\frac{4}{3}$$