Solve 44t^2-244t=0

$$44 t ^ { 2 } - 244 t = 0$$

Solve for t

$$t = \frac{61}{11} = 5\frac{6}{11} \approx 5.545454545$$

$$t=0$$

Steps Using Factoring

Factor out t.

$$t\left(44t-244\right)=0$$

To find equation solutions, solve t=0 and 44t-244=0.

$$t=0 t=\frac{61}{11}$$

Steps Using the Quadratic Formula

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.

$$44t^{2}-244t=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 44 for a, -244 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$t=\frac{-\left(-244\right)±\sqrt{\left(-244\right)^{2}}}{2\times 44}$$

Take the square root of \left(-244\right)^{2}.

$$t=\frac{-\left(-244\right)±244}{2\times 44}$$

The opposite of -244 is 244.

$$t=\frac{244±244}{2\times 44}$$

Multiply 2 times 44.

$$t=\frac{244±244}{88}$$

Now solve the equation t=\frac{244±244}{88} when ± is plus. Add 244 to 244.

$$t=\frac{488}{88}$$

Reduce the fraction \frac{488}{88} to lowest terms by extracting and canceling out 8.

$$t=\frac{61}{11}$$

Now solve the equation t=\frac{244±244}{88} when ± is minus. Subtract 244 from 244.

$$t=\frac{0}{88}$$

Divide 0 by 88.

$$t=0$$

The equation is now solved.

$$t=\frac{61}{11} t=0$$

Steps for Completing the Square

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.

$$44t^{2}-244t=0$$

Divide both sides by 44.

$$\frac{44t^{2}-244t}{44}=\frac{0}{44}$$

Dividing by 44 undoes the multiplication by 44.

$$t^{2}+\left(-\frac{244}{44}\right)t=\frac{0}{44}$$

Reduce the fraction \frac{-244}{44} to lowest terms by extracting and canceling out 4.

$$t^{2}-\frac{61}{11}t=\frac{0}{44}$$

Divide 0 by 44.

$$t^{2}-\frac{61}{11}t=0$$

Divide -\frac{61}{11}, the coefficient of the x term, by 2 to get -\frac{61}{22}. Then add the square of -\frac{61}{22} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$t^{2}-\frac{61}{11}t+\left(-\frac{61}{22}\right)^{2}=\left(-\frac{61}{22}\right)^{2}$$

Square -\frac{61}{22} by squaring both the numerator and the denominator of the fraction.

$$t^{2}-\frac{61}{11}t+\frac{3721}{484}=\frac{3721}{484}$$

Factor t^{2}-\frac{61}{11}t+\frac{3721}{484}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(t-\frac{61}{22}\right)^{2}=\frac{3721}{484}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(t-\frac{61}{22}\right)^{2}}=\sqrt{\frac{3721}{484}}$$

Simplify.

$$t-\frac{61}{22}=\frac{61}{22} t-\frac{61}{22}=-\frac{61}{22}$$

Add \frac{61}{22} to both sides of the equation.

$$t=\frac{61}{11} t=0$$