Solve s(t)=-16t^2+110t

$$s ( t ) = - 16 t ^ { 2 } + 110 t$$

Factor

$$2t\left(55-8t\right)$$

Solution Steps

Factor out 2.

$$2\left(-8t^{2}+55t\right)$$

Consider -8t^{2}+55t. Factor out t.

$$t\left(-8t+55\right)$$

Rewrite the complete factored expression.

$$2t\left(-8t+55\right)$$

Steps Using the Quadratic Formula

Quadratic polynomial can be factored using the transformation ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), where x_{1} and x_{2} are the solutions of the quadratic equation ax^{2}+bx+c=0.

$$-16t^{2}+110t=0$$

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.

$$t=\frac{-110±\sqrt{110^{2}}}{2\left(-16\right)}$$

Take the square root of 110^{2}.

$$t=\frac{-110±110}{2\left(-16\right)}$$

Multiply 2 times -16.

$$t=\frac{-110±110}{-32}$$

Now solve the equation t=\frac{-110±110}{-32} when ± is plus. Add -110 to 110.

$$t=\frac{0}{-32}$$

Divide 0 by -32.

$$t=0$$

Now solve the equation t=\frac{-110±110}{-32} when ± is minus. Subtract 110 from -110.

$$t=-\frac{220}{-32}$$

Reduce the fraction \frac{-220}{-32} to lowest terms by extracting and canceling out 4.

$$t=\frac{55}{8}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute 0 for x_{1} and \frac{55}{8} for x_{2}.

$$-16t^{2}+110t=-16t\left(t-\frac{55}{8}\right)$$

Subtract \frac{55}{8} from t by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$-16t^{2}+110t=-16t\times \frac{-8t+55}{-8}$$

Cancel out 8, the greatest common factor in -16 and -8.

$$-16t^{2}+110t=2t\left(-8t+55\right)$$

Evaluate

$$2t\left(55-8t\right)$$