SOLUTION: Please help me solve this, 5x^2 + 14x = -3

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Question 91107: Please help me solve this, 5x^2 + 14x = -3
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
5x%5E2+%2B+14x+=+-3
5x%5E2+%2B+14x+%2B3=0 Add 3 to both sides


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%2B14%2Ax%2B3=0 ( notice a=5, b=14, and c=3)

x+=+%28-14+%2B-+sqrt%28+%2814%29%5E2-4%2A5%2A3+%29%29%2F%282%2A5%29 Plug in a=5, b=14, and c=3



x+=+%28-14+%2B-+sqrt%28+196-4%2A5%2A3+%29%29%2F%282%2A5%29 Square 14 to get 196



x+=+%28-14+%2B-+sqrt%28+196%2B-60+%29%29%2F%282%2A5%29 Multiply -4%2A3%2A5 to get -60



x+=+%28-14+%2B-+sqrt%28+136+%29%29%2F%282%2A5%29 Combine like terms in the radicand (everything under the square root)



x+=+%28-14+%2B-+2%2Asqrt%2834%29%29%2F%282%2A5%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)



x+=+%28-14+%2B-+2%2Asqrt%2834%29%29%2F10 Multiply 2 and 5 to get 10

So now the expression breaks down into two parts

x+=+%28-14+%2B+2%2Asqrt%2834%29%29%2F10 or x+=+%28-14+-+2%2Asqrt%2834%29%29%2F10


Now break up the fraction


x=-14%2F10%2B2%2Asqrt%2834%29%2F10 or x=-14%2F10-2%2Asqrt%2834%29%2F10


Simplify


x=-7+%2F+5%2Bsqrt%2834%29%2F5 or x=-7+%2F+5-sqrt%2834%29%2F5


So these expressions approximate to

x=-0.23380962103094 or x=-2.56619037896906


So our solutions are:
x=-0.23380962103094 or x=-2.56619037896906

Notice when we graph 5%2Ax%5E2%2B14%2Ax%2B3, we get:



when we use the root finder feature on a calculator, we find that x=-0.23380962103094 and x=-2.56619037896906.So this verifies our answer