# Solve By Factoring Help Need

#### Ashley911

height of ball thrown = h
t = time in seconds

h = -4.9t^2 + 38t + 1.75

what is the time of the ball when h = 50

I need to be able to solve it by factoring? i can do it if the numbers 4.9 and 38 have a common denominator but can not do when they are decimals?
any help appreciated

Last edited:

#### e^(i*pi)

MHF Hall of Honor
height of ball thrown = h
t = time in seconds

h = -4.9t^2 + 38t + 1.75

what is the height of the ball after 3 seconds

I need to be able to solve it by factoring? i can do it if the numbers 4.9 and 38 have a common denominator but can do when they are decimals?
any help appreciated
$$\displaystyle h(t) = -4.9t^2 + 38t + 1.75$$

To find the height at 3 seconds solve $$\displaystyle h(3)$$ by putting in 3 wherever you find t in the original equation. No factoring required

$$\displaystyle h(3) = -4.9(3^2) + 38(3) + 1.75$$

Ashley911

#### Ashley911

I have to solve it by factoring its a homework question.

#### obesechicken13

I suppose you could plug in 50 for h, then subtract 50 from both sides

should look something like
-4.9t^2 + 38t - 48.25 = 0

Then just use the quadratic formula to find the two roots of this equation. Using those two roots, you can find the factors of the polynomial. One of those roots will be your time, (the positive one).

The quadratic formula will find your factors, however this is a bit redundant, since to find the factors you will need to find the roots, and one of the roots is your answer.

Otherwise you could use the decomposition method shown here: How to Factor Second Degree Polynomials (Quadratic Equations) - wikiHow

Ashley911

#### Ashley911

Thanks but am still stuck here is my issue

I need to find the two numbers that when multiplied = 4.9*48.25
and
when added together are = 48.25

I keep getting decimals and believe this should not be the case.

#### e^(i*pi)

MHF Hall of Honor
Thanks but am still stuck here is my issue

I need to find the two numbers that when multiplied = 4.9*48.25
and
when added together are = 48.25

I keep getting decimals and believe this should not be the case.
You won't get neat factors because $$\displaystyle b^2-4ac$$ is not a perfect square

Ashley911

#### rtblue

$$\displaystyle h = -4.9t^2 + 38t + 1.75$$

$$\displaystyle \frac{\-b\pm\sqrt{b^2-4ac}}{2a}$$

plug in the values to get

$$\displaystyle \frac{-38\pm\sqrt{38^2-4(-4.9)(1.75)}}{2(-4.90)}$$

Now solve for both values: + and -

Ashley911

#### e^(i*pi)

MHF Hall of Honor
The OP could also complete the square - it's a kind of factoring

$$\displaystyle 50 = -4.9t^2 + 38t + 1.75$$

$$\displaystyle 4.9t^2-38t = -48.25$$

$$\displaystyle t^2 - \frac{38}{4.9} = -\frac{48.25}{4.9}$$

$$\displaystyle \left(t- \frac{38}{9.8}\right)^2 - \left(\frac{38}{4.9}\right)^2 = -\frac{48.25}{4.9}$$

$$\displaystyle \left(t- \frac{38}{9.8}\right)^2 = \left(\frac{38}{4.9}\right)^2 -\frac{48.25}{4.9}$$

$$\displaystyle t - \frac{38}{9.8} = \pm \sqrt{ \left(\frac{38}{4.9} \right)^2 -\frac{48.25}{4.9}}$$

$$\displaystyle t = \frac{38}{9.8} \pm \sqrt{ \left(\frac{38}{4.9} \right)^2 -\frac{48.25}{4.9}}$$

Ashley911