Solve 9x^2-17=0

$$9 x ^ { 2 } - 17 = 0$$

Solve for x

$$x = \frac{\sqrt{17}}{3} \approx 1.374368542$$

$$x = -\frac{\sqrt{17}}{3} \approx -1.374368542$$

Steps by Finding Square Root

Add 17 to both sides. Anything plus zero gives itself.

$$9x^{2}=17$$

Divide both sides by 9.

$$x^{2}=\frac{17}{9}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{17}}{3} x=-\frac{\sqrt{17}}{3}$$

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.

$$9x^{2}-17=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 9 for a, 0 for b, and -17 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 9\left(-17\right)}}{2\times 9}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 9\left(-17\right)}}{2\times 9}$$

Multiply -4 times 9.

$$x=\frac{0±\sqrt{-36\left(-17\right)}}{2\times 9}$$

Multiply -36 times -17.

$$x=\frac{0±\sqrt{612}}{2\times 9}$$

Take the square root of 612.

$$x=\frac{0±6\sqrt{17}}{2\times 9}$$

Multiply 2 times 9.

$$x=\frac{0±6\sqrt{17}}{18}$$

Now solve the equation x=\frac{0±6\sqrt{17}}{18} when ± is plus.

$$x=\frac{\sqrt{17}}{3}$$

Now solve the equation x=\frac{0±6\sqrt{17}}{18} when ± is minus.

$$x=-\frac{\sqrt{17}}{3}$$

The equation is now solved.

$$x=\frac{\sqrt{17}}{3} x=-\frac{\sqrt{17}}{3}$$