Solve t=0.63845t^2

$$t = 0.63845 t ^ { 2 }$$

Solve for t

$$t = \frac{20000}{12769} = 1\frac{7231}{12769} \approx 1.566293367$$

$$t=0$$

Steps Using Factoring

Subtract 0.63845t^{2} from both sides.

$$t-0.63845t^{2}=0$$

Factor out t.

$$t\left(1-0.63845t\right)=0$$

To find equation solutions, solve t=0 and 1-\frac{12769t}{20000}=0.

$$t=0 t=\frac{20000}{12769}$$

Steps Using the Quadratic Formula

Subtract 0.63845t^{2} from both sides.

$$t-0.63845t^{2}=0$$

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

$$-0.63845t^{2}+t=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -0.63845 for a, 1 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$t=\frac{-1±\sqrt{1^{2}}}{2\left(-0.63845\right)}$$

Take the square root of 1^{2}.

$$t=\frac{-1±1}{2\left(-0.63845\right)}$$

Multiply 2 times -0.63845.

$$t=\frac{-1±1}{-1.2769}$$

Now solve the equation t=\frac{-1±1}{-1.2769} when ± is plus. Add -1 to 1.

$$t=\frac{0}{-1.2769}$$

Divide 0 by -1.2769 by multiplying 0 by the reciprocal of -1.2769.

$$t=0$$

Now solve the equation t=\frac{-1±1}{-1.2769} when ± is minus. Subtract 1 from -1.

$$t=-\frac{2}{-1.2769}$$

Divide -2 by -1.2769 by multiplying -2 by the reciprocal of -1.2769.

$$t=\frac{20000}{12769}$$

The equation is now solved.

$$t=0 t=\frac{20000}{12769}$$

Steps for Completing the Square

Subtract 0.63845t^{2} from both sides.

$$t-0.63845t^{2}=0$$

Quadratic equations such as this one can be solved by completing the square. In order to complete the square, the equation must first be in the form x^{2}+bx=c.

$$-0.63845t^{2}+t=0$$

Divide both sides of the equation by -0.63845, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{-0.63845t^{2}+t}{-0.63845}=\frac{0}{-0.63845}$$

Dividing by -0.63845 undoes the multiplication by -0.63845.

$$t^{2}+\frac{1}{-0.63845}t=\frac{0}{-0.63845}$$

Divide 1 by -0.63845 by multiplying 1 by the reciprocal of -0.63845.

$$t^{2}-\frac{20000}{12769}t=\frac{0}{-0.63845}$$

Divide 0 by -0.63845 by multiplying 0 by the reciprocal of -0.63845.

$$t^{2}-\frac{20000}{12769}t=0$$

Divide -\frac{20000}{12769}, the coefficient of the x term, by 2 to get -\frac{10000}{12769}. Then add the square of -\frac{10000}{12769} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$t^{2}-\frac{20000}{12769}t+\left(-\frac{10000}{12769}\right)^{2}=\left(-\frac{10000}{12769}\right)^{2}$$

Square -\frac{10000}{12769} by squaring both the numerator and the denominator of the fraction.

$$t^{2}-\frac{20000}{12769}t+\frac{100000000}{163047361}=\frac{100000000}{163047361}$$

Factor t^{2}-\frac{20000}{12769}t+\frac{100000000}{163047361}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(t-\frac{10000}{12769}\right)^{2}=\frac{100000000}{163047361}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(t-\frac{10000}{12769}\right)^{2}}=\sqrt{\frac{100000000}{163047361}}$$

Simplify.

$$t-\frac{10000}{12769}=\frac{10000}{12769} t-\frac{10000}{12769}=-\frac{10000}{12769}$$

Add \frac{10000}{12769} to both sides of the equation.

$$t=\frac{20000}{12769} t=0$$