Solve 17k^2+22kk+1=0

$$17 k ^ { 2 } + 22 k k + 1 = 0$$

Solve for k

$$k=-\frac{\sqrt{39}i}{39}\approx -0-0.160128154i$$

$$k=\frac{\sqrt{39}i}{39}\approx 0.160128154i$$

Steps by Finding Square Root

Multiply k and k to get k^{2}.

$$17k^{2}+22k^{2}+1=0$$

Combine 17k^{2} and 22k^{2} to get 39k^{2}.

$$39k^{2}+1=0$$

Subtract 1 from both sides. Anything subtracted from zero gives its negation.

$$39k^{2}=-1$$

Divide both sides by 39.

$$k^{2}=-\frac{1}{39}$$

The equation is now solved.

$$k=\frac{\sqrt{39}i}{39} k=-\frac{\sqrt{39}i}{39}$$

Steps Using the Quadratic Formula

Multiply k and k to get k^{2}.

$$17k^{2}+22k^{2}+1=0$$

Combine 17k^{2} and 22k^{2} to get 39k^{2}.

$$39k^{2}+1=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 39 for a, 0 for b, and 1 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$k=\frac{0±\sqrt{0^{2}-4\times 39}}{2\times 39}$$

Square 0.

$$k=\frac{0±\sqrt{-4\times 39}}{2\times 39}$$

Multiply -4 times 39.

$$k=\frac{0±\sqrt{-156}}{2\times 39}$$

Take the square root of -156.

$$k=\frac{0±2\sqrt{39}i}{2\times 39}$$

Multiply 2 times 39.

$$k=\frac{0±2\sqrt{39}i}{78}$$

Now solve the equation k=\frac{0±2\sqrt{39}i}{78} when ± is plus.

$$k=\frac{\sqrt{39}i}{39}$$

Now solve the equation k=\frac{0±2\sqrt{39}i}{78} when ± is minus.

$$k=-\frac{\sqrt{39}i}{39}$$

The equation is now solved.

$$k=\frac{\sqrt{39}i}{39} k=-\frac{\sqrt{39}i}{39}$$