Solve 7x^2=-48

$$7 x ^ { 2 } = - 48$$

Solve for x (complex solution)

$$x=-\frac{4\sqrt{21}i}{7}\approx -0-2.618614683i$$

$$x=\frac{4\sqrt{21}i}{7}\approx 2.618614683i$$

Steps by Finding Square Root

Divide both sides by 7.

$$x^{2}=-\frac{48}{7}$$

The equation is now solved.

$$x=\frac{4\sqrt{21}i}{7} x=-\frac{4\sqrt{21}i}{7}$$

Steps Using the Quadratic Formula

Divide both sides by 7.

$$x^{2}=-\frac{48}{7}$$

Add \frac{48}{7} to both sides.

$$x^{2}+\frac{48}{7}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and \frac{48}{7} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{48}{7}}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times \frac{48}{7}}}{2}$$

Multiply -4 times \frac{48}{7}.

$$x=\frac{0±\sqrt{-\frac{192}{7}}}{2}$$

Take the square root of -\frac{192}{7}.

$$x=\frac{0±\frac{8\sqrt{21}i}{7}}{2}$$

Now solve the equation x=\frac{0±\frac{8\sqrt{21}i}{7}}{2} when ± is plus.

$$x=\frac{4\sqrt{21}i}{7}$$

Now solve the equation x=\frac{0±\frac{8\sqrt{21}i}{7}}{2} when ± is minus.

$$x=-\frac{4\sqrt{21}i}{7}$$

The equation is now solved.

$$x=\frac{4\sqrt{21}i}{7} x=-\frac{4\sqrt{21}i}{7}$$