Solve 10x^2+3=633

$$10 { x }^{ 2 } +3=633$$

Solve for x

$$x=3\sqrt{7}\approx 7.937253933$$

$$x=-3\sqrt{7}\approx -7.937253933$$

Steps by Finding Square Root

Subtract 3 from both sides.

$$10x^{2}=633-3$$

Subtract 3 from 633 to get 630.

$$10x^{2}=630$$

Divide both sides by 10.

$$x^{2}=\frac{630}{10}$$

Divide 630 by 10 to get 63.

$$x^{2}=63$$

Take the square root of both sides of the equation.

$$x=3\sqrt{7} x=-3\sqrt{7}$$

Steps Using the Quadratic Formula

Subtract 633 from both sides.

$$10x^{2}+3-633=0$$

Subtract 633 from 3 to get -630.

$$10x^{2}-630=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 10 for a, 0 for b, and -630 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 10\left(-630\right)}}{2\times 10}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 10\left(-630\right)}}{2\times 10}$$

Multiply -4 times 10.

$$x=\frac{0±\sqrt{-40\left(-630\right)}}{2\times 10}$$

Multiply -40 times -630.

$$x=\frac{0±\sqrt{25200}}{2\times 10}$$

Take the square root of 25200.

$$x=\frac{0±60\sqrt{7}}{2\times 10}$$

Multiply 2 times 10.

$$x=\frac{0±60\sqrt{7}}{20}$$

Now solve the equation x=\frac{0±60\sqrt{7}}{20} when ± is plus.

$$x=3\sqrt{7}$$

Now solve the equation x=\frac{0±60\sqrt{7}}{20} when ± is minus.

$$x=-3\sqrt{7}$$

The equation is now solved.

$$x=3\sqrt{7} x=-3\sqrt{7}$$