Solve 46x^2=-1024

$$46 { x }^{ 2 } =-1024$$

Solve for x (complex solution)

$$x=-\frac{16\sqrt{46}i}{23}\approx -0-4.718142597i$$

$$x=\frac{16\sqrt{46}i}{23}\approx 4.718142597i$$

Steps by Finding Square Root

Divide both sides by 46.

$$x^{2}=\frac{-1024}{46}$$

Reduce the fraction \frac{-1024}{46} to lowest terms by extracting and canceling out 2.

$$x^{2}=-\frac{512}{23}$$

The equation is now solved.

$$x=\frac{16\sqrt{46}i}{23} x=-\frac{16\sqrt{46}i}{23}$$

Steps Using the Quadratic Formula

Divide both sides by 46.

$$x^{2}=\frac{-1024}{46}$$

Reduce the fraction \frac{-1024}{46} to lowest terms by extracting and canceling out 2.

$$x^{2}=-\frac{512}{23}$$

Add \frac{512}{23} to both sides.

$$x^{2}+\frac{512}{23}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and \frac{512}{23} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{512}{23}}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times \frac{512}{23}}}{2}$$

Multiply -4 times \frac{512}{23}.

$$x=\frac{0±\sqrt{-\frac{2048}{23}}}{2}$$

Take the square root of -\frac{2048}{23}.

$$x=\frac{0±\frac{32\sqrt{46}i}{23}}{2}$$

Now solve the equation x=\frac{0±\frac{32\sqrt{46}i}{23}}{2} when ± is plus.

$$x=\frac{16\sqrt{46}i}{23}$$

Now solve the equation x=\frac{0±\frac{32\sqrt{46}i}{23}}{2} when ± is minus.

$$x=-\frac{16\sqrt{46}i}{23}$$

The equation is now solved.

$$x=\frac{16\sqrt{46}i}{23} x=-\frac{16\sqrt{46}i}{23}$$