Solve 0=4-0*x-0.5*9.8066*x^2

$$0=4-0 \times x-0.5 \times 9.8066 \times { x }^{ 2 }$$

Solve for x

$$x=\frac{200\sqrt{49033}}{49033}\approx 0.903203814$$

$$x=-\frac{200\sqrt{49033}}{49033}\approx -0.903203814$$

Steps by Finding Square Root

Anything times zero gives zero.

$$0=4-0-0.5\times 9.8066x^{2}$$

Subtract 0 from 4 to get 4.

$$0=4-0.5\times 9.8066x^{2}$$

Multiply 0.5 and 9.8066 to get 4.9033.

$$0=4-4.9033x^{2}$$

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

$$4-4.9033x^{2}=0$$

Subtract 4 from both sides. Anything subtracted from zero gives its negation.

$$-4.9033x^{2}=-4$$

Divide both sides by -4.9033.

$$x^{2}=\frac{-4}{-4.9033}$$

Expand \frac{-4}{-4.9033} by multiplying both numerator and the denominator by 10000.

$$x^{2}=\frac{-40000}{-49033}$$

Fraction \frac{-40000}{-49033} can be simplified to \frac{40000}{49033} by removing the negative sign from both the numerator and the denominator.

$$x^{2}=\frac{40000}{49033}$$

Take the square root of both sides of the equation.

$$x=\frac{200\sqrt{49033}}{49033} x=-\frac{200\sqrt{49033}}{49033}$$

Steps Using the Quadratic Formula

Anything times zero gives zero.

$$0=4-0-0.5\times 9.8066x^{2}$$

Subtract 0 from 4 to get 4.

$$0=4-0.5\times 9.8066x^{2}$$

Multiply 0.5 and 9.8066 to get 4.9033.

$$0=4-4.9033x^{2}$$

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

$$4-4.9033x^{2}=0$$

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.

$$-4.9033x^{2}+4=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -4.9033 for a, 0 for b, and 4 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-4.9033\right)\times 4}}{2\left(-4.9033\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-4.9033\right)\times 4}}{2\left(-4.9033\right)}$$

Multiply -4 times -4.9033.

$$x=\frac{0±\sqrt{19.6132\times 4}}{2\left(-4.9033\right)}$$

Multiply 19.6132 times 4.

$$x=\frac{0±\sqrt{78.4528}}{2\left(-4.9033\right)}$$

Take the square root of 78.4528.

$$x=\frac{0±\frac{\sqrt{49033}}{25}}{2\left(-4.9033\right)}$$

Multiply 2 times -4.9033.

$$x=\frac{0±\frac{\sqrt{49033}}{25}}{-9.8066}$$

Now solve the equation x=\frac{0±\frac{\sqrt{49033}}{25}}{-9.8066} when ± is plus.

$$x=-\frac{200\sqrt{49033}}{49033}$$

Now solve the equation x=\frac{0±\frac{\sqrt{49033}}{25}}{-9.8066} when ± is minus.

$$x=\frac{200\sqrt{49033}}{49033}$$

The equation is now solved.

$$x=-\frac{200\sqrt{49033}}{49033} x=\frac{200\sqrt{49033}}{49033}$$