Solve 5/2*x^2+56=0

$$\frac{ 5 }{ 2 } \times { x }^{ 2 } +56=0$$

Solve for x (complex solution)

$$x=-\frac{4\sqrt{35}i}{5}\approx -0-4.732863826i$$

$$x=\frac{4\sqrt{35}i}{5}\approx 4.732863826i$$

Steps by Finding Square Root

Subtract 56 from both sides. Anything subtracted from zero gives its negation.

$$\frac{5}{2}x^{2}=-56$$

Multiply both sides by \frac{2}{5}, the reciprocal of \frac{5}{2}.

$$x^{2}=-56\times \frac{2}{5}$$

Multiply -56 and \frac{2}{5} to get -\frac{112}{5}.

$$x^{2}=-\frac{112}{5}$$

The equation is now solved.

$$x=\frac{4\sqrt{35}i}{5} x=-\frac{4\sqrt{35}i}{5}$$

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.

$$\frac{5}{2}x^{2}+56=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{5}{2} for a, 0 for b, and 56 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{5}{2}\times 56}}{2\times \frac{5}{2}}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times \frac{5}{2}\times 56}}{2\times \frac{5}{2}}$$

Multiply -4 times \frac{5}{2}.

$$x=\frac{0±\sqrt{-10\times 56}}{2\times \frac{5}{2}}$$

Multiply -10 times 56.

$$x=\frac{0±\sqrt{-560}}{2\times \frac{5}{2}}$$

Take the square root of -560.

$$x=\frac{0±4\sqrt{35}i}{2\times \frac{5}{2}}$$

Multiply 2 times \frac{5}{2}.

$$x=\frac{0±4\sqrt{35}i}{5}$$

Now solve the equation x=\frac{0±4\sqrt{35}i}{5} when ± is plus.

$$x=\frac{4\sqrt{35}i}{5}$$

Now solve the equation x=\frac{0±4\sqrt{35}i}{5} when ± is minus.

$$x=-\frac{4\sqrt{35}i}{5}$$

The equation is now solved.

$$x=\frac{4\sqrt{35}i}{5} x=-\frac{4\sqrt{35}i}{5}$$