Solve 17x^2+16=0

$$17 x ^ { 2 } + 16 = 0$$

Solve for x (complex solution)

$$x=-\frac{4\sqrt{17}i}{17}\approx -0-0.9701425i$$

$$x=\frac{4\sqrt{17}i}{17}\approx 0.9701425i$$

Steps by Finding Square Root

Subtract 16 from both sides. Anything subtracted from zero gives its negation.

$$17x^{2}=-16$$

Divide both sides by 17.

$$x^{2}=-\frac{16}{17}$$

The equation is now solved.

$$x=\frac{4\sqrt{17}i}{17} x=-\frac{4\sqrt{17}i}{17}$$

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.

$$17x^{2}+16=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 17 for a, 0 for b, and 16 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 17\times 16}}{2\times 17}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 17\times 16}}{2\times 17}$$

Multiply -4 times 17.

$$x=\frac{0±\sqrt{-68\times 16}}{2\times 17}$$

Multiply -68 times 16.

$$x=\frac{0±\sqrt{-1088}}{2\times 17}$$

Take the square root of -1088.

$$x=\frac{0±8\sqrt{17}i}{2\times 17}$$

Multiply 2 times 17.

$$x=\frac{0±8\sqrt{17}i}{34}$$

Now solve the equation x=\frac{0±8\sqrt{17}i}{34} when ± is plus.

$$x=\frac{4\sqrt{17}i}{17}$$

Now solve the equation x=\frac{0±8\sqrt{17}i}{34} when ± is minus.

$$x=-\frac{4\sqrt{17}i}{17}$$

The equation is now solved.

$$x=\frac{4\sqrt{17}i}{17} x=-\frac{4\sqrt{17}i}{17}$$