Solve 29x^2=-40

$$29 x ^ { 2 } = - 40$$

Solve for x (complex solution)

$$x=-\frac{2\sqrt{290}i}{29}\approx -0-1.174440439i$$

$$x=\frac{2\sqrt{290}i}{29}\approx 1.174440439i$$

Steps by Finding Square Root

Divide both sides by 29.

$$x^{2}=-\frac{40}{29}$$

The equation is now solved.

$$x=\frac{2\sqrt{290}i}{29} x=-\frac{2\sqrt{290}i}{29}$$

Steps Using the Quadratic Formula

Divide both sides by 29.

$$x^{2}=-\frac{40}{29}$$

Add \frac{40}{29} to both sides.

$$x^{2}+\frac{40}{29}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and \frac{40}{29} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{40}{29}}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times \frac{40}{29}}}{2}$$

Multiply -4 times \frac{40}{29}.

$$x=\frac{0±\sqrt{-\frac{160}{29}}}{2}$$

Take the square root of -\frac{160}{29}.

$$x=\frac{0±\frac{4\sqrt{290}i}{29}}{2}$$

Now solve the equation x=\frac{0±\frac{4\sqrt{290}i}{29}}{2} when ± is plus.

$$x=\frac{2\sqrt{290}i}{29}$$

Now solve the equation x=\frac{0±\frac{4\sqrt{290}i}{29}}{2} when ± is minus.

$$x=-\frac{2\sqrt{290}i}{29}$$

The equation is now solved.

$$x=\frac{2\sqrt{290}i}{29} x=-\frac{2\sqrt{290}i}{29}$$