SOLUTION: please help me solve this problem using the quadratic formula. 5x^2 - 3x - 3 = 0

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Question 92079This question is from textbook Algebra and Trigonometry
: please help me solve this problem using the quadratic formula.
5x^2 - 3x - 3 = 0 This question is from textbook Algebra and Trigonometry

Found 2 solutions by funmath, jim_thompson5910:
Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
please help me solve this problem using the quadratic formula.
5x^2 - 3x - 3 = 0
Solved by pluggable solver: SOLVE quadratic equation with variable
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+=+5%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

Happy Calculating!!!

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let's use the quadratic formula to solve for x:


Starting with the general quadratic

ax%5E2%2Bbx%2Bc=0

the general solution using the quadratic equation is:

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29

So lets solve 5%2Ax%5E2-3%2Ax-3=0 ( notice a=5, b=-3, and c=-3)

x+=+%28--3+%2B-+sqrt%28+%28-3%29%5E2-4%2A5%2A-3+%29%29%2F%282%2A5%29 Plug in a=5, b=-3, and c=-3



x+=+%283+%2B-+sqrt%28+%28-3%29%5E2-4%2A5%2A-3+%29%29%2F%282%2A5%29 Negate -3 to get 3



x+=+%283+%2B-+sqrt%28+9-4%2A5%2A-3+%29%29%2F%282%2A5%29 Square -3 to get 9 (note: remember when you square -3, you must square the negative as well. This is because %28-3%29%5E2=-3%2A-3=9.)



x+=+%283+%2B-+sqrt%28+9%2B60+%29%29%2F%282%2A5%29 Multiply -4%2A-3%2A5 to get 60



x+=+%283+%2B-+sqrt%28+69+%29%29%2F%282%2A5%29 Combine like terms in the radicand (everything under the square root)






x+=+%283+%2B-+sqrt%2869%29%29%2F10 Multiply 2 and 5 to get 10

So now the expression breaks down into two parts

x+=+%283+%2B+sqrt%2869%29%29%2F10 or x+=+%283+-+sqrt%2869%29%29%2F10


Now break up the fraction


x=%2B3%2F10%2Bsqrt%2869%29%2F10 or x=%2B3%2F10-sqrt%2869%29%2F10





So these expressions approximate to

x=1.13066238629181 or x=-0.530662386291808


So our solutions are:
x=1.13066238629181 or x=-0.530662386291808

Notice when we graph 5%2Ax%5E2-3%2Ax-3, we get:



when we use the root finder feature on a calculator, we find that x=1.13066238629181 and x=-0.530662386291808.So this verifies our answer