Solve 28+2x^2=5

$$28+2 { x }^{ 2 } =5$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{46}i}{2}\approx -0-3.391164992i$$

$$x=\frac{\sqrt{46}i}{2}\approx 3.391164992i$$

Steps by Finding Square Root

Subtract 28 from both sides.

$$2x^{2}=5-28$$

Subtract 28 from 5 to get -23.

$$2x^{2}=-23$$

Divide both sides by 2.

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

The equation is now solved.

$$x=\frac{\sqrt{46}i}{2} x=-\frac{\sqrt{46}i}{2}$$

Steps Using the Quadratic Formula

Subtract 5 from both sides.

$$28+2x^{2}-5=0$$

Subtract 5 from 28 to get 23.

$$23+2x^{2}=0$$

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.

$$2x^{2}+23=0$$

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

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

Square 0.

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

Multiply -4 times 2.

$$x=\frac{0±\sqrt{-8\times 23}}{2\times 2}$$

Multiply -8 times 23.

$$x=\frac{0±\sqrt{-184}}{2\times 2}$$

Take the square root of -184.

$$x=\frac{0±2\sqrt{46}i}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{0±2\sqrt{46}i}{4}$$

Now solve the equation x=\frac{0±2\sqrt{46}i}{4} when ± is plus.

$$x=\frac{\sqrt{46}i}{2}$$

Now solve the equation x=\frac{0±2\sqrt{46}i}{4} when ± is minus.

$$x=-\frac{\sqrt{46}i}{2}$$

The equation is now solved.

$$x=\frac{\sqrt{46}i}{2} x=-\frac{\sqrt{46}i}{2}$$