Solve 35x^2=-27

$$35 x ^ { 2 } = - 27$$

Solve for x (complex solution)

$$x=-\frac{3\sqrt{105}i}{35}\approx -0-0.878310066i$$

$$x=\frac{3\sqrt{105}i}{35}\approx 0.878310066i$$

Steps by Finding Square Root

Divide both sides by 35.

$$x^{2}=-\frac{27}{35}$$

The equation is now solved.

$$x=\frac{3\sqrt{105}i}{35} x=-\frac{3\sqrt{105}i}{35}$$

Steps Using the Quadratic Formula

Divide both sides by 35.

$$x^{2}=-\frac{27}{35}$$

Add \frac{27}{35} to both sides.

$$x^{2}+\frac{27}{35}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and \frac{27}{35} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{27}{35}}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times \frac{27}{35}}}{2}$$

Multiply -4 times \frac{27}{35}.

$$x=\frac{0±\sqrt{-\frac{108}{35}}}{2}$$

Take the square root of -\frac{108}{35}.

$$x=\frac{0±\frac{6\sqrt{105}i}{35}}{2}$$

Now solve the equation x=\frac{0±\frac{6\sqrt{105}i}{35}}{2} when ± is plus.

$$x=\frac{3\sqrt{105}i}{35}$$

Now solve the equation x=\frac{0±\frac{6\sqrt{105}i}{35}}{2} when ± is minus.

$$x=-\frac{3\sqrt{105}i}{35}$$

The equation is now solved.

$$x=\frac{3\sqrt{105}i}{35} x=-\frac{3\sqrt{105}i}{35}$$