SOLUTION: How do I solve x^2+6x+4=0 in quadratc formula? I think this is how to slove x= -6+or-√6^2-4(x)(4)/2(x) -6+or-√36-4(x)(4)/2(x)

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: How do I solve x^2+6x+4=0 in quadratc formula? I think this is how to slove x= -6+or-√6^2-4(x)(4)/2(x) -6+or-√36-4(x)(4)/2(x)       Log On


   

Question 117555: How do I solve x^2+6x+4=0 in quadratc formula?
I think this is how to slove x= -6+or-√6^2-4(x)(4)/2(x)
-6+or-√36-4(x)(4)/2(x)
-6+or-√36-16/2(x)
-6+or-√20/2
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 x%5E2%2B6%2Ax%2B4=0 ( notice a=1, b=6, and c=4)




x+=+%28-6+%2B-+sqrt%28+%286%29%5E2-4%2A1%2A4+%29%29%2F%282%2A1%29 Plug in a=1, b=6, and c=4



x+=+%28-6+%2B-+sqrt%28+36-4%2A1%2A4+%29%29%2F%282%2A1%29 Square 6 to get 36



x+=+%28-6+%2B-+sqrt%28+36%2B-16+%29%29%2F%282%2A1%29 Multiply -4%2A4%2A1 to get -16



x+=+%28-6+%2B-+sqrt%28+20+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)



x+=+%28-6+%2B-+2%2Asqrt%285%29%29%2F%282%2A1%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)



x+=+%28-6+%2B-+2%2Asqrt%285%29%29%2F2 Multiply 2 and 1 to get 2

So now the expression breaks down into two parts

x+=+%28-6+%2B+2%2Asqrt%285%29%29%2F2 or x+=+%28-6+-+2%2Asqrt%285%29%29%2F2


Now break up the fraction


x=-6%2F2%2B2%2Asqrt%285%29%2F2 or x=-6%2F2-2%2Asqrt%285%29%2F2


Simplify


x=-3%2Bsqrt%285%29 or x=-3-sqrt%285%29


So these expressions approximate to

x=-0.76393202250021 or x=-5.23606797749979


So our solutions are:
x=-0.76393202250021 or x=-5.23606797749979

Notice when we graph x%5E2%2B6%2Ax%2B4, we get:



when we use the root finder feature on a calculator, we find that x=-0.76393202250021 and x=-5.23606797749979.So this verifies our answer