Solve 0=40-4.9x^2

$$0=40-4.9 { x }^{ 2 }$$

Solve for x

$$x = \frac{20}{7} = 2\frac{6}{7} \approx 2.857142857$$

$$x = -\frac{20}{7} = -2\frac{6}{7} \approx -2.857142857$$

Steps by Finding Square Root

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

$$40-4.9x^{2}=0$$

Subtract 40 from both sides. Anything subtracted from zero gives its negation.

$$-4.9x^{2}=-40$$

Divide both sides by -4.9.

$$x^{2}=\frac{-40}{-4.9}$$

Expand \frac{-40}{-4.9} by multiplying both numerator and the denominator by 10.

$$x^{2}=\frac{-400}{-49}$$

Fraction \frac{-400}{-49} can be simplified to \frac{400}{49} by removing the negative sign from both the numerator and the denominator.

$$x^{2}=\frac{400}{49}$$

Take the square root of both sides of the equation.

$$x=\frac{20}{7} x=-\frac{20}{7}$$

Steps Using the Quadratic Formula

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

$$40-4.9x^{2}=0$$

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.

$$-4.9x^{2}+40=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -4.9 for a, 0 for b, and 40 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-4.9\right)\times 40}}{2\left(-4.9\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-4.9\right)\times 40}}{2\left(-4.9\right)}$$

Multiply -4 times -4.9.

$$x=\frac{0±\sqrt{19.6\times 40}}{2\left(-4.9\right)}$$

Multiply 19.6 times 40.

$$x=\frac{0±\sqrt{784}}{2\left(-4.9\right)}$$

Take the square root of 784.

$$x=\frac{0±28}{2\left(-4.9\right)}$$

Multiply 2 times -4.9.

$$x=\frac{0±28}{-9.8}$$

Now solve the equation x=\frac{0±28}{-9.8} when ± is plus. Divide 28 by -9.8 by multiplying 28 by the reciprocal of -9.8.

$$x=-\frac{20}{7}$$

Now solve the equation x=\frac{0±28}{-9.8} when ± is minus. Divide -28 by -9.8 by multiplying -28 by the reciprocal of -9.8.

$$x=\frac{20}{7}$$

The equation is now solved.

$$x=-\frac{20}{7} x=\frac{20}{7}$$