Solve x^2+9x^2+17=0

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

Solve for x (complex solution)

$$x=-\frac{\sqrt{170}i}{10}\approx -0-1.303840481i$$

$$x=\frac{\sqrt{170}i}{10}\approx 1.303840481i$$

Steps by Finding Square Root

Combine x^{2} and 9x^{2} to get 10x^{2}.

$$10x^{2}+17=0$$

Subtract 17 from both sides. Anything subtracted from zero gives its negation.

$$10x^{2}=-17$$

Divide both sides by 10.

$$x^{2}=-\frac{17}{10}$$

The equation is now solved.

$$x=\frac{\sqrt{170}i}{10} x=-\frac{\sqrt{170}i}{10}$$

Steps Using the Quadratic Formula

Combine x^{2} and 9x^{2} to get 10x^{2}.

$$10x^{2}+17=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 10 for a, 0 for b, and 17 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 10\times 17}}{2\times 10}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 10\times 17}}{2\times 10}$$

Multiply -4 times 10.

$$x=\frac{0±\sqrt{-40\times 17}}{2\times 10}$$

Multiply -40 times 17.

$$x=\frac{0±\sqrt{-680}}{2\times 10}$$

Take the square root of -680.

$$x=\frac{0±2\sqrt{170}i}{2\times 10}$$

Multiply 2 times 10.

$$x=\frac{0±2\sqrt{170}i}{20}$$

Now solve the equation x=\frac{0±2\sqrt{170}i}{20} when ± is plus.

$$x=\frac{\sqrt{170}i}{10}$$

Now solve the equation x=\frac{0±2\sqrt{170}i}{20} when ± is minus.

$$x=-\frac{\sqrt{170}i}{10}$$

The equation is now solved.

$$x=\frac{\sqrt{170}i}{10} x=-\frac{\sqrt{170}i}{10}$$