SOLUTION: Solve 25x^2-125x+144=0 by using the quadratic formula a) x=3.2 or x=1.8 b) x=-3.2 or x=1.8 c)x=3.2 or x =-1.8 d)x=-3.2 orx =-1.8

Question 597494: Solve 25x^2-125x+144=0 by using the quadratic formula
a) x=3.2 or x=1.8
b) x=-3.2 or x=1.8
c)x=3.2 or x =-1.8
d)x=-3.2 orx =-1.8

Found 2 solutions by jim_thompson5910, KMST:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Start with the given equation.

Notice that the quadratic is in the form of where , , and

Let's use the quadratic formula to solve for "x":

Start with the quadratic formula

Plug in , , and

Negate to get .

Square to get .

Multiply to get

Subtract from to get

Multiply and to get .

Take the square root of to get .

or Break up the expression.

or Combine like terms.

or Simplify.

So the solutions are or

In decimal form, the solutions are or

So the answer is choice A

Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
If this is a homework problem, to practice using the quadratic formula, practice as long as you can. Practice is good.
If you have a problem like this in a multiple choice test, and do not need to show your work, you could pick the right answer without going through the work.
It may look like cheating, but it may be worthwhile saving time on one problem so that you can complete the other problems and get a better grade.
(I never cared much for grades, but they can open or close doors for you).
Sometimes it is very easy to verify that one of the multiple choices is the solution and prove that the others are wrong.
Sometimes you can work backwards from the answer to the question.
This problem is one of those times.
All the choices given have the same absolute values, differing only in the signs. That allows you to pick the right answer without doing any calculation.

SHORTCUT/CHEAT:
You probably know that if choice a) was the answer, the equation could be factored into
25(x-3.2)(x-1.8)=0
Mutliplying would give you
and
with a negative coefficient for the tern in x

and a positive independent term at the end

There is no need to even calculate the numbers; knowing the signs is enough.
Choice b) and choice c) would result in a negative independent term, so they are not the answer.
Choice d) would mean that the equation could be factored into
25(x+3.2)(x+1.8)=0
and the equation would have all plus signs, as in
, but that was not the equation.
Only choice a) works.
Since the -125 in -125x is negative and the -144 at the end is positive, the solutions had to be both positive as in choice a). Unless you were asked to show your work, there was no need to calculate anything.
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