SOLUTION: Solve by using the quadratic formula. 2x^2 + 5x = 4

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Question 88257: Solve by using the quadratic formula. 2x^2 + 5x = 4

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
2x%5E2+%2B+5x+=+4

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

Now let's use the quadratic formula to solve for x:


Starting with the general quadratic

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

the general form of 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%2F%282%2A2%29 Simplify 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


Which 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