Solve 5x^2-50=0

$$5 x ^ { 2 } - 50 = 0$$

Solve for x

$$x=\sqrt{10}\approx 3.16227766$$

$$x=-\sqrt{10}\approx -3.16227766$$

Steps by Finding Square Root

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

$$5x^{2}=50$$

Divide both sides by 5.

$$x^{2}=\frac{50}{5}$$

Divide 50 by 5 to get 10.

$$x^{2}=10$$

Take the square root of both sides of the equation.

$$x=\sqrt{10} x=-\sqrt{10}$$

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.

$$5x^{2}-50=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 5 for a, 0 for b, and -50 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 5\left(-50\right)}}{2\times 5}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 5\left(-50\right)}}{2\times 5}$$

Multiply -4 times 5.

$$x=\frac{0±\sqrt{-20\left(-50\right)}}{2\times 5}$$

Multiply -20 times -50.

$$x=\frac{0±\sqrt{1000}}{2\times 5}$$

Take the square root of 1000.

$$x=\frac{0±10\sqrt{10}}{2\times 5}$$

Multiply 2 times 5.

$$x=\frac{0±10\sqrt{10}}{10}$$

Now solve the equation x=\frac{0±10\sqrt{10}}{10} when ± is plus.

$$x=\sqrt{10}$$

Now solve the equation x=\frac{0±10\sqrt{10}}{10} when ± is minus.

$$x=-\sqrt{10}$$

The equation is now solved.

$$x=\sqrt{10} x=-\sqrt{10}$$