Solve 2x^2+3=1933

$$2 x ^ { 2 } + 3 = 1933$$

Solve for x

$$x=\sqrt{965}\approx 31.064449134$$

$$x=-\sqrt{965}\approx -31.064449134$$

Steps by Finding Square Root

Subtract 3 from both sides.

$$2x^{2}=1933-3$$

Subtract 3 from 1933 to get 1930.

$$2x^{2}=1930$$

Divide both sides by 2.

$$x^{2}=\frac{1930}{2}$$

Divide 1930 by 2 to get 965.

$$x^{2}=965$$

Take the square root of both sides of the equation.

$$x=\sqrt{965} x=-\sqrt{965}$$

Steps Using the Quadratic Formula

Subtract 1933 from both sides.

$$2x^{2}+3-1933=0$$

Subtract 1933 from 3 to get -1930.

$$2x^{2}-1930=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and -1930 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\left(-1930\right)}}{2\times 2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 2\left(-1930\right)}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{0±\sqrt{-8\left(-1930\right)}}{2\times 2}$$

Multiply -8 times -1930.

$$x=\frac{0±\sqrt{15440}}{2\times 2}$$

Take the square root of 15440.

$$x=\frac{0±4\sqrt{965}}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{0±4\sqrt{965}}{4}$$

Now solve the equation x=\frac{0±4\sqrt{965}}{4} when ± is plus.

$$x=\sqrt{965}$$

Now solve the equation x=\frac{0±4\sqrt{965}}{4} when ± is minus.

$$x=-\sqrt{965}$$

The equation is now solved.

$$x=\sqrt{965} x=-\sqrt{965}$$