Solve 0=10-98x^2

$$0=10-98 { x }^{ 2 }$$

Solve for x

$$x=\frac{\sqrt{5}}{7}\approx 0.319438282$$

$$x=-\frac{\sqrt{5}}{7}\approx -0.319438282$$

Steps by Finding Square Root

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

$$10-98x^{2}=0$$

Subtract 10 from both sides. Anything subtracted from zero gives its negation.

$$-98x^{2}=-10$$

Divide both sides by -98.

$$x^{2}=\frac{-10}{-98}$$

Reduce the fraction \frac{-10}{-98} to lowest terms by extracting and canceling out -2.

$$x^{2}=\frac{5}{49}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{5}}{7} x=-\frac{\sqrt{5}}{7}$$

Steps Using the Quadratic Formula

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

$$10-98x^{2}=0$$

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.

$$-98x^{2}+10=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -98 for a, 0 for b, and 10 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-98\right)\times 10}}{2\left(-98\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-98\right)\times 10}}{2\left(-98\right)}$$

Multiply -4 times -98.

$$x=\frac{0±\sqrt{392\times 10}}{2\left(-98\right)}$$

Multiply 392 times 10.

$$x=\frac{0±\sqrt{3920}}{2\left(-98\right)}$$

Take the square root of 3920.

$$x=\frac{0±28\sqrt{5}}{2\left(-98\right)}$$

Multiply 2 times -98.

$$x=\frac{0±28\sqrt{5}}{-196}$$

Now solve the equation x=\frac{0±28\sqrt{5}}{-196} when ± is plus.

$$x=-\frac{\sqrt{5}}{7}$$

Now solve the equation x=\frac{0±28\sqrt{5}}{-196} when ± is minus.

$$x=\frac{\sqrt{5}}{7}$$

The equation is now solved.

$$x=-\frac{\sqrt{5}}{7} x=\frac{\sqrt{5}}{7}$$