SOLUTION: Use the quadratic formula to solve the equation. 2x^2+12x= -5

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Question 116587: Use the quadratic formula to solve the equation.
2x^2+12x= -5
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

2x%5E2%2B12x=-5 Start with the given equation


2x%5E2%2B12x%2B5=0 Move all of the terms to the left side


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 2%2Ax%5E2%2B12%2Ax%2B5=0 ( notice a=2, b=12, and c=5)




x+=+%28-12+%2B-+sqrt%28+%2812%29%5E2-4%2A2%2A5+%29%29%2F%282%2A2%29 Plug in a=2, b=12, and c=5



x+=+%28-12+%2B-+sqrt%28+144-4%2A2%2A5+%29%29%2F%282%2A2%29 Square 12 to get 144



x+=+%28-12+%2B-+sqrt%28+144%2B-40+%29%29%2F%282%2A2%29 Multiply -4%2A5%2A2 to get -40



x+=+%28-12+%2B-+sqrt%28+104+%29%29%2F%282%2A2%29 Combine like terms in the radicand (everything under the square root)



x+=+%28-12+%2B-+2%2Asqrt%2826%29%29%2F%282%2A2%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)



x+=+%28-12+%2B-+2%2Asqrt%2826%29%29%2F4 Multiply 2 and 2 to get 4

So now the expression breaks down into two parts

x+=+%28-12+%2B+2%2Asqrt%2826%29%29%2F4 or x+=+%28-12+-+2%2Asqrt%2826%29%29%2F4


Now break up the fraction


x=-12%2F4%2B2%2Asqrt%2826%29%2F4 or x=-12%2F4-2%2Asqrt%2826%29%2F4


Simplify


x=-3%2Bsqrt%2826%29%2F2 or x=-3-sqrt%2826%29%2F2


So these expressions approximate to

x=-0.450490243203608 or x=-5.54950975679639


So our solutions are:
x=-0.450490243203608 or x=-5.54950975679639

Notice when we graph 2%2Ax%5E2%2B12%2Ax%2B5, we get:



when we use the root finder feature on a calculator, we find that x=-0.450490243203608 and x=-5.54950975679639.So this verifies our answer