SOLUTION: {{{49a^2 + 16 = 56a}}}

Algebra ->  Algebra  -> Polynomials-and-rational-expressions -> SOLUTION: {{{49a^2 + 16 = 56a}}}      Log On

Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!
Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!

   

Question 27020: 49a%5E2+%2B+16+=+56a
Answer by mbarugel(146) About Me  (Show Source):
You can put this solution on YOUR website!
First we subtract 56a from both sides, getting:
49a%5E2+-56a+%2B+16+=+0
Then we follow the standard procedure for solving quadratic equations:
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 49x%5E2%2B-56x%2B16+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-56%29%5E2-4%2A49%2A16=0.

Discriminant d=0 is zero! That means that there is only one solution: x+=+%28-%28-56%29%29%2F2%5C49.
Expression can be factored: 49x%5E2%2B-56x%2B16+=+%28x-0.571428571428571%29%2A%28x-0.571428571428571%29

Again, the answer is: 0.571428571428571, 0.571428571428571. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+49%2Ax%5E2%2B-56%2Ax%2B16+%29