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

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Question 201639: solve the equation with the quadratic formula:
8r^2=9
Found 2 solutions by Alan3354, jim_thompson5910:
Answer by Alan3354(69443) 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 ax%5E2%2Bbx%2Bc=0 (in our case 8x%5E2%2B0x%2B-9+=+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=%280%29%5E2-4%2A8%2A-9=288.

Discriminant d=288 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-0%2B-sqrt%28+288+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%280%29%2Bsqrt%28+288+%29%29%2F2%5C8+=+1.06066017177982
x%5B2%5D+=+%28-%280%29-sqrt%28+288+%29%29%2F2%5C8+=+-1.06066017177982

Quadratic expression 8x%5E2%2B0x%2B-9 can be factored:
8x%5E2%2B0x%2B-9+=+%28x-1.06066017177982%29%2A%28x--1.06066017177982%29
Again, the answer is: 1.06066017177982, -1.06066017177982. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+8%2Ax%5E2%2B0%2Ax%2B-9+%29

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

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

8r%5E2=9 Start with the given equation.


8r%5E2-9=0 Subtract 9 from both sides.


Notice that the quadratic 8r%5E2-9 is in the form of Ar%5E2%2BBr%2BC where A=8, B=0, and C=-9


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


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


r+=+%28-%280%29+%2B-+sqrt%28+%280%29%5E2-4%288%29%28-9%29+%29%29%2F%282%288%29%29 Plug in A=8, B=0, and C=-9


r+=+%280+%2B-+sqrt%28+0-4%288%29%28-9%29+%29%29%2F%282%288%29%29 Square 0 to get 0.


r+=+%280+%2B-+sqrt%28+0--288+%29%29%2F%282%288%29%29 Multiply 4%288%29%28-9%29 to get -288


r+=+%280+%2B-+sqrt%28+0%2B288+%29%29%2F%282%288%29%29 Rewrite sqrt%280--288%29 as sqrt%280%2B288%29


r+=+%280+%2B-+sqrt%28+288+%29%29%2F%282%288%29%29 Add 0 to 288 to get 288


r+=+%280+%2B-+sqrt%28+288+%29%29%2F%2816%29 Multiply 2 and 8 to get 16.


r+=+%280+%2B-+12%2Asqrt%282%29%29%2F%2816%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


r+=+%2812%2Asqrt%282%29%29%2F%2816%29 or r+=+-%2812%2Asqrt%282%29%29%2F%2816%29 Break up the expression.


r+=+%283%2F4%29%2Asqrt%282%29 or r+=+-%283%2F4%29%2Asqrt%282%29 Reduce.


So the solutions are r+=+%283%2F4%29%2Asqrt%282%29 or r+=+-%283%2F4%29%2Asqrt%282%29