SOLUTION: solve the equation with the quadratic formula: 8r^2=9

Algebra ->  Algebra  -> Quadratic Equations and Parabolas -> SOLUTION: solve the equation with the quadratic formula: 8r^2=9      Log On

Ad: You enter your algebra equation or inequality - Algebrator solves it step-by-step while providing clear explanations. Free on-line demo .
Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!
Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!

   

Question 201639: solve the equation with the quadratic formula:
8r^2=9
Found 2 solutions by Alan3354, jim_thompson5910:
Answer by Alan3354(5863) About Me  (Show Source):
You can put this solution on YOUR website!
8r^2=9
8x^2 - 9 = 0 (the solver uses x as default)
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=288 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 1.06066017177982, -1.06066017177982. Here's your graph:

------------
It doesn't reduce, either.
r = +3sqrt(2)/4
r = -3sqrt(2)/4

Answer by jim_thompson5910(13679) About Me  (Show Source):
You can put this solution on YOUR website!

Start with the given equation.


Subtract 9 from both sides.


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


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


Start with the quadratic formula


Plug in , , and


Square to get .


Multiply to get


Rewrite as


Add to to get


Multiply and to get .


Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


or Break up the expression.


or Reduce.


So the solutions are or