Solve 2.46t^2=24.6t

$$2.46 t ^ { 2 } = 24.6 t$$

Solve for t

$$t=10$$

$$t=0$$

Steps Using Factoring

Subtract 24.6t from both sides.

$$2.46t^{2}-24.6t=0$$

Factor out t.

$$t\left(2.46t-24.6\right)=0$$

To find equation solutions, solve t=0 and \frac{123t}{50}-24.6=0.

$$t=0 t=10$$

Steps Using the Quadratic Formula

Subtract 24.6t from both sides.

$$2.46t^{2}-24.6t=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2.46 for a, -24.6 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$t=\frac{-\left(-24.6\right)±\sqrt{\left(-24.6\right)^{2}}}{2\times 2.46}$$

Take the square root of \left(-24.6\right)^{2}.

$$t=\frac{-\left(-24.6\right)±\frac{123}{5}}{2\times 2.46}$$

The opposite of -24.6 is 24.6.

$$t=\frac{24.6±\frac{123}{5}}{2\times 2.46}$$

Multiply 2 times 2.46.

$$t=\frac{24.6±\frac{123}{5}}{4.92}$$

Now solve the equation t=\frac{24.6±\frac{123}{5}}{4.92} when ± is plus. Add 24.6 to \frac{123}{5} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$t=\frac{\frac{246}{5}}{4.92}$$

Divide \frac{246}{5} by 4.92 by multiplying \frac{246}{5} by the reciprocal of 4.92.

$$t=10$$

Now solve the equation t=\frac{24.6±\frac{123}{5}}{4.92} when ± is minus. Subtract \frac{123}{5} from 24.6 by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$t=\frac{0}{4.92}$$

Divide 0 by 4.92 by multiplying 0 by the reciprocal of 4.92.

$$t=0$$

The equation is now solved.

$$t=10 t=0$$

Steps for Completing the Square

Subtract 24.6t from both sides.

$$2.46t^{2}-24.6t=0$$

Divide both sides of the equation by 2.46, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{2.46t^{2}-24.6t}{2.46}=\frac{0}{2.46}$$

Dividing by 2.46 undoes the multiplication by 2.46.

$$t^{2}+\left(-\frac{24.6}{2.46}\right)t=\frac{0}{2.46}$$

Divide -24.6 by 2.46 by multiplying -24.6 by the reciprocal of 2.46.

$$t^{2}-10t=\frac{0}{2.46}$$

Divide 0 by 2.46 by multiplying 0 by the reciprocal of 2.46.

$$t^{2}-10t=0$$

Divide -10, the coefficient of the x term, by 2 to get -5. Then add the square of -5 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$t^{2}-10t+\left(-5\right)^{2}=\left(-5\right)^{2}$$

Square -5.

$$t^{2}-10t+25=25$$

Factor t^{2}-10t+25. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(t-5\right)^{2}=25$$

Take the square root of both sides of the equation.

$$\sqrt{\left(t-5\right)^{2}}=\sqrt{25}$$

Simplify.

$$t-5=5 t-5=-5$$

Add 5 to both sides of the equation.

$$t=10 t=0$$