Solve 2x^2+4=396

$$2 x ^ { 2 } + 4 = 396$$

Solve for x

$$x=14$$

$$x=-14$$

Steps Using Difference of Squares

Subtract 396 from both sides.

$$2x^{2}+4-396=0$$

Subtract 396 from 4 to get -392.

$$2x^{2}-392=0$$

Divide both sides by 2.

$$x^{2}-196=0$$

Consider x^{2}-196. Rewrite x^{2}-196 as x^{2}-14^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-14\right)\left(x+14\right)=0$$

To find equation solutions, solve x-14=0 and x+14=0.

$$x=14 x=-14$$

Steps by Finding Square Root

Subtract 4 from both sides.

$$2x^{2}=396-4$$

Subtract 4 from 396 to get 392.

$$2x^{2}=392$$

Divide both sides by 2.

$$x^{2}=\frac{392}{2}$$

Divide 392 by 2 to get 196.

$$x^{2}=196$$

Take the square root of both sides of the equation.

$$x=14 x=-14$$

Steps Using the Quadratic Formula

Subtract 396 from both sides.

$$2x^{2}+4-396=0$$

Subtract 396 from 4 to get -392.

$$2x^{2}-392=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and -392 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\left(-392\right)}}{2\times 2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 2\left(-392\right)}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{0±\sqrt{-8\left(-392\right)}}{2\times 2}$$

Multiply -8 times -392.

$$x=\frac{0±\sqrt{3136}}{2\times 2}$$

Take the square root of 3136.

$$x=\frac{0±56}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{0±56}{4}$$

Now solve the equation x=\frac{0±56}{4} when ± is plus. Divide 56 by 4.

$$x=14$$

Now solve the equation x=\frac{0±56}{4} when ± is minus. Divide -56 by 4.

$$x=-14$$

The equation is now solved.

$$x=14 x=-14$$