Solve 0=100-1/2*9.81*x^2

$$0=100- \frac{ 1 }{ 2 } \times 9.81 \times { x }^{ 2 }$$

Solve for x

$$x = \frac{100 \sqrt{218}}{327} \approx 4.51523641$$

$$x = -\frac{100 \sqrt{218}}{327} \approx -4.51523641$$

Steps by Finding Square Root

Multiply \frac{1}{2} and 9.81 to get \frac{981}{200}.

$$0=100-\frac{981}{200}x^{2}$$

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

$$100-\frac{981}{200}x^{2}=0$$

Subtract 100 from both sides. Anything subtracted from zero gives its negation.

$$-\frac{981}{200}x^{2}=-100$$

Multiply both sides by -\frac{200}{981}, the reciprocal of -\frac{981}{200}.

$$x^{2}=-100\left(-\frac{200}{981}\right)$$

Multiply -100 and -\frac{200}{981} to get \frac{20000}{981}.

$$x^{2}=\frac{20000}{981}$$

Take the square root of both sides of the equation.

$$x=\frac{100\sqrt{218}}{327} x=-\frac{100\sqrt{218}}{327}$$

Steps Using the Quadratic Formula

Multiply \frac{1}{2} and 9.81 to get \frac{981}{200}.

$$0=100-\frac{981}{200}x^{2}$$

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

$$100-\frac{981}{200}x^{2}=0$$

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.

$$-\frac{981}{200}x^{2}+100=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -\frac{981}{200} for a, 0 for b, and 100 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{981}{200}\right)\times 100}}{2\left(-\frac{981}{200}\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{981}{200}\right)\times 100}}{2\left(-\frac{981}{200}\right)}$$

Multiply -4 times -\frac{981}{200}.

$$x=\frac{0±\sqrt{\frac{981}{50}\times 100}}{2\left(-\frac{981}{200}\right)}$$

Multiply \frac{981}{50} times 100.

$$x=\frac{0±\sqrt{1962}}{2\left(-\frac{981}{200}\right)}$$

Take the square root of 1962.

$$x=\frac{0±3\sqrt{218}}{2\left(-\frac{981}{200}\right)}$$

Multiply 2 times -\frac{981}{200}.

$$x=\frac{0±3\sqrt{218}}{-\frac{981}{100}}$$

Now solve the equation x=\frac{0±3\sqrt{218}}{-\frac{981}{100}} when ± is plus.

$$x=-\frac{100\sqrt{218}}{327}$$

Now solve the equation x=\frac{0±3\sqrt{218}}{-\frac{981}{100}} when ± is minus.

$$x=\frac{100\sqrt{218}}{327}$$

The equation is now solved.

$$x=-\frac{100\sqrt{218}}{327} x=\frac{100\sqrt{218}}{327}$$