Solve 9x^2=25

$$9 x ^ { 2 } = 25$$

Solve for x

$$x = \frac{5}{3} = 1\frac{2}{3} \approx 1.666666667$$

$$x = -\frac{5}{3} = -1\frac{2}{3} \approx -1.666666667$$

Steps Using Difference of Squares

Divide both sides by 9.

$$x^{2}=\frac{25}{9}$$

Subtract \frac{25}{9} from both sides.

$$x^{2}-\frac{25}{9}=0$$

Multiply both sides by 9.

$$9x^{2}-25=0$$

Consider 9x^{2}-25. Rewrite 9x^{2}-25 as \left(3x\right)^{2}-5^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(3x-5\right)\left(3x+5\right)=0$$

To find equation solutions, solve 3x-5=0 and 3x+5=0.

$$x=\frac{5}{3} x=-\frac{5}{3}$$

Steps by Finding Square Root

Divide both sides by 9.

$$x^{2}=\frac{25}{9}$$

Take the square root of both sides of the equation.

$$x=\frac{5}{3} x=-\frac{5}{3}$$

Steps Using the Quadratic Formula

Divide both sides by 9.

$$x^{2}=\frac{25}{9}$$

Subtract \frac{25}{9} from both sides.

$$x^{2}-\frac{25}{9}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{25}{9} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{25}{9}\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{25}{9}\right)}}{2}$$

Multiply -4 times -\frac{25}{9}.

$$x=\frac{0±\sqrt{\frac{100}{9}}}{2}$$

Take the square root of \frac{100}{9}.

$$x=\frac{0±\frac{10}{3}}{2}$$

Now solve the equation x=\frac{0±\frac{10}{3}}{2} when ± is plus.

$$x=\frac{5}{3}$$

Now solve the equation x=\frac{0±\frac{10}{3}}{2} when ± is minus.

$$x=-\frac{5}{3}$$

The equation is now solved.

$$x=\frac{5}{3} x=-\frac{5}{3}$$