SOLUTION: Solve using the quadratic formula. 5x^2-3x-3=0

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Question 166534: Solve using the quadratic formula.
5x^2-3x-3=0
Found 2 solutions by Alan3354, jim_thompson5910:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Solve using the quadratic formula.
5x^2-3x-3=0
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Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 5x%5E2%2B-3x%2B-3+=+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=%28-3%29%5E2-4%2A5%2A-3=69.

Discriminant d=69 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--3%2B-sqrt%28+69+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-3%29%2Bsqrt%28+69+%29%29%2F2%5C5+=+1.13066238629181
x%5B2%5D+=+%28-%28-3%29-sqrt%28+69+%29%29%2F2%5C5+=+-0.530662386291808

Quadratic expression 5x%5E2%2B-3x%2B-3 can be factored:
5x%5E2%2B-3x%2B-3+=+%28x-1.13066238629181%29%2A%28x--0.530662386291808%29
Again, the answer is: 1.13066238629181, -0.530662386291808. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+5%2Ax%5E2%2B-3%2Ax%2B-3+%29

Ignore the onsite solver's comments about factoring, it's only correct when the coefficient of the x^2 term is 1.

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
5x%5E2-3x-3=0 Start with the given equation.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=5, b=-3, and c=-3


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-%28-3%29+%2B-+sqrt%28+%28-3%29%5E2-4%285%29%28-3%29+%29%29%2F%282%285%29%29 Plug in a=5, b=-3, and c=-3


x+=+%283+%2B-+sqrt%28+%28-3%29%5E2-4%285%29%28-3%29+%29%29%2F%282%285%29%29 Negate -3 to get 3.


x+=+%283+%2B-+sqrt%28+9-4%285%29%28-3%29+%29%29%2F%282%285%29%29 Square -3 to get 9.


x+=+%283+%2B-+sqrt%28+9--60+%29%29%2F%282%285%29%29 Multiply 4%285%29%28-3%29 to get -60


x+=+%283+%2B-+sqrt%28+9%2B60+%29%29%2F%282%285%29%29 Rewrite sqrt%289--60%29 as sqrt%289%2B60%29


x+=+%283+%2B-+sqrt%28+69+%29%29%2F%282%285%29%29 Add 9 to 60 to get 69


x+=+%283+%2B-+sqrt%28+69+%29%29%2F%2810%29 Multiply 2 and 5 to get 10.


x+=+%283%2Bsqrt%2869%29%29%2F%2810%29 or x+=+%283-sqrt%2869%29%29%2F%2810%29 Break up the expression.


So the answers are x+=+%283%2Bsqrt%2869%29%29%2F%2810%29 or x+=+%283-sqrt%2869%29%29%2F%2810%29


which approximate to x=1.131 or x=-0.531