SOLUTION: Solve. x^2 + 6x -4 = 0 Here's what I think is the answer. Can someone tell me if I'm on the right track? (-6 + sqrt (52)/2) (-6 - sqrt ( 52 )/2)

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Solve. x^2 + 6x -4 = 0 Here's what I think is the answer. Can someone tell me if I'm on the right track? (-6 + sqrt (52)/2) (-6 - sqrt ( 52 )/2)      Log On


   

Question 133182: Solve.
x^2 + 6x -4 = 0
Here's what I think is the answer. Can someone tell me if I'm on the right track?
(-6 + sqrt (52)/2) (-6 - sqrt ( 52 )/2)
Found 2 solutions by vleith, jim_thompson5910:
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
You're on the right track, but you've got an error.
You used the quadratic equation, which is correct.
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
However, note that the entire answer is over 2a. Not just the radical portion. So the -6 in your answers need to be divided by 2. Also, yo can simplfy sqrt%2852%29 into sqrt%284%29sqrt%2813%29
My answers are:
-3+%2B+sqrt%2852%29%2F2 and -3+-+sqrt%2852%29%2F2
-3+%2B+sqrt%2813%29 and -3+-+sqrt%2813%29

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-4=0 ( notice a=1, b=6, and c=-4)




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



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



x+=+%28-6+%2B-+sqrt%28+36%2B16+%29%29%2F%282%2A1%29 Multiply -4%2A-4%2A1 to get 16



x+=+%28-6+%2B-+sqrt%28+52+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)



x+=+%28-6+%2B-+2%2Asqrt%2813%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%2813%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%2813%29%29%2F2 or x+=+%28-6+-+2%2Asqrt%2813%29%29%2F2


Now break up the fraction


x=-6%2F2%2B2%2Asqrt%2813%29%2F2 or x=-6%2F2-2%2Asqrt%2813%29%2F2


Simplify


x=-3%2Bsqrt%2813%29 or x=-3-sqrt%2813%29


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Answer:



So the exact solutions are


x=-3%2Bsqrt%2813%29 or x=-3-sqrt%2813%29


So you are on the right track, but could simplify the answer.