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

Question 201639: solve the equation with the quadratic formula:
8r^2=9
Found 2 solutions by Alan3354, jim_thompson5910:
Answer by Alan3354(69443) (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:

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

Answer by jim_thompson5910(35256) (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

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