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

Algebra ->  Quadratic Equations and Parabolas -> 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       Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!

25x%5E2-125x%2B144=0 Start with the given equation.


Notice that the quadratic 25x%5E2-125x%2B144 is in the form of Ax%5E2%2BBx%2BC where A=25, B=-125, and C=144


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


x+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


x+=+%28-%28-125%29+%2B-+sqrt%28+%28-125%29%5E2-4%2825%29%28144%29+%29%29%2F%282%2825%29%29 Plug in A=25, B=-125, and C=144


x+=+%28125+%2B-+sqrt%28+%28-125%29%5E2-4%2825%29%28144%29+%29%29%2F%282%2825%29%29 Negate -125 to get 125.


x+=+%28125+%2B-+sqrt%28+15625-4%2825%29%28144%29+%29%29%2F%282%2825%29%29 Square -125 to get 15625.


x+=+%28125+%2B-+sqrt%28+15625-14400+%29%29%2F%282%2825%29%29 Multiply 4%2825%29%28144%29 to get 14400


x+=+%28125+%2B-+sqrt%28+1225+%29%29%2F%282%2825%29%29 Subtract 14400 from 15625 to get 1225


x+=+%28125+%2B-+sqrt%28+1225+%29%29%2F%2850%29 Multiply 2 and 25 to get 50.


x+=+%28125+%2B-+35%29%2F%2850%29 Take the square root of 1225 to get 35.


x+=+%28125+%2B+35%29%2F%2850%29 or x+=+%28125+-+35%29%2F%2850%29 Break up the expression.


x+=+%28160%29%2F%2850%29 or x+=++%2890%29%2F%2850%29 Combine like terms.


x+=+16%2F5 or x+=+9%2F5 Simplify.


So the solutions are x+=+16%2F5 or x+=+9%2F5

In decimal form, the solutions are x=3.2 or x=1.8

So the answer is choice A


Answer by KMST(5328) About Me  (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
25%28x%5E2-%283.2%2B1.8%29x%2B3.2%2A1.8%29=0 and 25x%5E2-25%283.2%2B1.8%29x%2B25%2A3.2%2A1.8%29=0
with a negative coefficient for the tern in x
-25%283.2%2B1.8%29x=-25%2A5%2Ax=-125x
and a positive independent term at the end
25%2A3.2%2A1.8=144
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
25x%5E2%2B125x%2B144=0, 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.