Solve 10x^2-50=0

$$10 x ^ { 2 } - 50 = 0$$

Solve for x

$$x=\sqrt{5}\approx 2.236067977$$

$$x=-\sqrt{5}\approx -2.236067977$$

Steps by Finding Square Root

Add 50 to both sides. Anything plus zero gives itself.

$$10x^{2}=50$$

Divide both sides by 10.

$$x^{2}=\frac{50}{10}$$

Divide 50 by 10 to get 5.

$$x^{2}=5$$

Take the square root of both sides of the equation.

$$x=\sqrt{5} x=-\sqrt{5}$$

Steps Using the Quadratic Formula

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$10x^{2}-50=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 10 for a, 0 for b, and -50 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 10\left(-50\right)}}{2\times 10}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 10\left(-50\right)}}{2\times 10}$$

Multiply -4 times 10.

$$x=\frac{0±\sqrt{-40\left(-50\right)}}{2\times 10}$$

Multiply -40 times -50.

$$x=\frac{0±\sqrt{2000}}{2\times 10}$$

Take the square root of 2000.

$$x=\frac{0±20\sqrt{5}}{2\times 10}$$

Multiply 2 times 10.

$$x=\frac{0±20\sqrt{5}}{20}$$

Now solve the equation x=\frac{0±20\sqrt{5}}{20} when ± is plus.

$$x=\sqrt{5}$$

Now solve the equation x=\frac{0±20\sqrt{5}}{20} when ± is minus.

$$x=-\sqrt{5}$$

The equation is now solved.

$$x=\sqrt{5} x=-\sqrt{5}$$