Solve 0=10-9.8x^2

$$0=10-9.8 { x }^{ 2 }$$

Solve for x

$$x = \frac{5 \sqrt{2}}{7} \approx 1.010152545$$

$$x = -\frac{5 \sqrt{2}}{7} \approx -1.010152545$$

Steps by Finding Square Root

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

$$10-9.8x^{2}=0$$

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

$$-9.8x^{2}=-10$$

Divide both sides by -9.8.

$$x^{2}=\frac{-10}{-9.8}$$

Expand \frac{-10}{-9.8} by multiplying both numerator and the denominator by 10.

$$x^{2}=\frac{-100}{-98}$$

Reduce the fraction \frac{-100}{-98} to lowest terms by extracting and canceling out -2.

$$x^{2}=\frac{50}{49}$$

Take the square root of both sides of the equation.

$$x=\frac{5\sqrt{2}}{7} x=-\frac{5\sqrt{2}}{7}$$

Steps Using the Quadratic Formula

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

$$10-9.8x^{2}=0$$

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.

$$-9.8x^{2}+10=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -9.8 for a, 0 for b, and 10 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-9.8\right)\times 10}}{2\left(-9.8\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-9.8\right)\times 10}}{2\left(-9.8\right)}$$

Multiply -4 times -9.8.

$$x=\frac{0±\sqrt{39.2\times 10}}{2\left(-9.8\right)}$$

Multiply 39.2 times 10.

$$x=\frac{0±\sqrt{392}}{2\left(-9.8\right)}$$

Take the square root of 392.

$$x=\frac{0±14\sqrt{2}}{2\left(-9.8\right)}$$

Multiply 2 times -9.8.

$$x=\frac{0±14\sqrt{2}}{-19.6}$$

Now solve the equation x=\frac{0±14\sqrt{2}}{-19.6} when ± is plus.

$$x=-\frac{5\sqrt{2}}{7}$$

Now solve the equation x=\frac{0±14\sqrt{2}}{-19.6} when ± is minus.

$$x=\frac{5\sqrt{2}}{7}$$

The equation is now solved.

$$x=-\frac{5\sqrt{2}}{7} x=\frac{5\sqrt{2}}{7}$$