SOLUTION: Could some one please help me solve this equation using the quadratic equation? {{{2x^2+5x=4}}}

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Question 102617: Could some one please help me solve this equation using the quadratic equation? 2x%5E2%2B5x=4
Found 2 solutions by jim_thompson5910, edjones:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
2x%5E2%2B5x=4 Start with the given equation

2x%5E2%2B5x-4=0 Subtract 4 from both sides



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 2%2Ax%5E2%2B5%2Ax-4=0 ( notice a=2, b=5, and c=-4)




x+=+%28-5+%2B-+sqrt%28+%285%29%5E2-4%2A2%2A-4+%29%29%2F%282%2A2%29 Plug in a=2, b=5, and c=-4



x+=+%28-5+%2B-+sqrt%28+25-4%2A2%2A-4+%29%29%2F%282%2A2%29 Square 5 to get 25



x+=+%28-5+%2B-+sqrt%28+25%2B32+%29%29%2F%282%2A2%29 Multiply -4%2A-4%2A2 to get 32



x+=+%28-5+%2B-+sqrt%28+57+%29%29%2F%282%2A2%29 Combine like terms in the radicand (everything under the square root)




x+=+%28-5+%2B-+sqrt%2857%29%29%2F4 Multiply 2 and 2 to get 4

So now the expression breaks down into two parts

x+=+%28-5+%2B+sqrt%2857%29%29%2F4 or x+=+%28-5+-+sqrt%2857%29%29%2F4


Now break up the fraction


x=-5%2F4%2Bsqrt%2857%29%2F4 or x=-5%2F4-sqrt%2857%29%2F4




So these expressions approximate to

x=0.637458608817687 or x=-3.13745860881769


So our solutions are:
x=0.637458608817687 or x=-3.13745860881769

Notice when we graph 2%2Ax%5E2%2B5%2Ax-4, we get:



when we use the root finder feature on a calculator, we find that x=0.637458608817687 and x=-3.13745860881769.So this verifies our answer

Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
2x%5E2%2B5x=4
2x^2+5x-4=0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B5x%2B-4+=+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=%285%29%5E2-4%2A2%2A-4=57.

Discriminant d=57 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-5%2B-sqrt%28+57+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%285%29%2Bsqrt%28+57+%29%29%2F2%5C2+=+0.637458608817687
x%5B2%5D+=+%28-%285%29-sqrt%28+57+%29%29%2F2%5C2+=+-3.13745860881769

Quadratic expression 2x%5E2%2B5x%2B-4 can be factored:
2x%5E2%2B5x%2B-4+=+%28x-0.637458608817687%29%2A%28x--3.13745860881769%29
Again, the answer is: 0.637458608817687, -3.13745860881769. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B5%2Ax%2B-4+%29