Solve 784=2x^2

$$784 = 2 x ^ { 2 }$$

Solve for x

$$x=14\sqrt{2}\approx 19.798989873$$

$$x=-14\sqrt{2}\approx -19.798989873$$

Steps by Finding Square Root

Divide both sides by 2.

$$\frac{784}{2}=x^{2}$$

Divide 784 by 2 to get 392.

$$392=x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$x^{2}=392$$

Take the square root of both sides of the equation.

$$x=14\sqrt{2} x=-14\sqrt{2}$$

Steps Using the Quadratic Formula

Divide both sides by 2.

$$\frac{784}{2}=x^{2}$$

Divide 784 by 2 to get 392.

$$392=x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$x^{2}=392$$

Subtract 392 from both sides.

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

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -392 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

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

Square 0.

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

Multiply -4 times -392.

$$x=\frac{0±\sqrt{1568}}{2}$$

Take the square root of 1568.

$$x=\frac{0±28\sqrt{2}}{2}$$

Now solve the equation x=\frac{0±28\sqrt{2}}{2} when ± is plus.

$$x=14\sqrt{2}$$

Now solve the equation x=\frac{0±28\sqrt{2}}{2} when ± is minus.

$$x=-14\sqrt{2}$$

The equation is now solved.

$$x=14\sqrt{2} x=-14\sqrt{2}$$