Solve 2x^2+40^2+4=298

$$2 x ^ { 2 } + 40 ^ { 2 } + 4 = 298$$

Solve for x (complex solution)

$$x=-\sqrt{653}i\approx -0-25.553864678i$$

$$x=\sqrt{653}i\approx 25.553864678i$$

Steps by Finding Square Root

Calculate 40 to the power of 2 and get 1600.

$$2x^{2}+1600+4=298$$

Add 1600 and 4 to get 1604.

$$2x^{2}+1604=298$$

Subtract 1604 from both sides.

$$2x^{2}=298-1604$$

Subtract 1604 from 298 to get -1306.

$$2x^{2}=-1306$$

Divide both sides by 2.

$$x^{2}=\frac{-1306}{2}$$

Divide -1306 by 2 to get -653.

$$x^{2}=-653$$

The equation is now solved.

$$x=\sqrt{653}i x=-\sqrt{653}i$$

Steps Using the Quadratic Formula

Calculate 40 to the power of 2 and get 1600.

$$2x^{2}+1600+4=298$$

Add 1600 and 4 to get 1604.

$$2x^{2}+1604=298$$

Subtract 298 from both sides.

$$2x^{2}+1604-298=0$$

Subtract 298 from 1604 to get 1306.

$$2x^{2}+1306=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and 1306 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\times 1306}}{2\times 2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 2\times 1306}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{0±\sqrt{-8\times 1306}}{2\times 2}$$

Multiply -8 times 1306.

$$x=\frac{0±\sqrt{-10448}}{2\times 2}$$

Take the square root of -10448.

$$x=\frac{0±4\sqrt{653}i}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{0±4\sqrt{653}i}{4}$$

Now solve the equation x=\frac{0±4\sqrt{653}i}{4} when ± is plus.

$$x=\sqrt{653}i$$

Now solve the equation x=\frac{0±4\sqrt{653}i}{4} when ± is minus.

$$x=-\sqrt{653}i$$

The equation is now solved.

$$x=\sqrt{653}i x=-\sqrt{653}i$$