SOLUTION: Choose the one alternative that best completes the statement or answers the question. Solve by completing the square. x^2 - 6x - 40 = 0 a) 10, -4 b) -10, 4 c)(-36

Algebra ->  Equations -> SOLUTION: Choose the one alternative that best completes the statement or answers the question. Solve by completing the square. x^2 - 6x - 40 = 0 a) 10, -4 b) -10, 4 c)(-36      Log On


   

Question 93105: Choose the one alternative that best completes the statement or answers the question.
Solve by completing the square.
x^2 - 6x - 40 = 0
a) 10, -4 b) -10, 4 c)(-36, -4 d) square root of -40, negative square root of -40
I think the answer is d after I plugged in all the options, but I don't know how to prove it. When I try to use completing the square I get up to this point, 6 plus or minus the square root of 160 over 2 and I can't go any further. Thanks so much!!
Found 3 solutions by stanbon, tutorcecilia, jim_thompson5910:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Solve by completing the square.
x^2 - 6x - 40 = 0
x^2-6x+? = 40+?
x^2+6x+[(1/2)6]^2 = 40 + [(1/2)6]^2
x^2+6x+9 = 40+9
(x+3)^2 = 49
x+3 = 7 or x+3 = -7
x = 4 or x = -10
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Cheers,
Stan H.

Answer by tutorcecilia(2152) About Me  (Show Source):
You can put this solution on YOUR website!
x^2 - 6x - 40+40 =40
x^2-6x=40
%28x%5E2-6x%2B%286%2F2%29%5E2%29}=%2840%2B%286%2F2%29%5E2%29

%28x%5E2-6x%2B%283%29%5E2%29=%2840%2B%283%29%5E2%29
%28x%5E2-6x%2B%283%29%5E2%29= %2840%2B%289%29%29
%28x%5E2-6x%2B%283%29%5E2%29=49
%28x-3%29%28x-3%29%29=49 [factor]
%28x-3%29%5E2%29= 49
%28sqrt%28%28x-3%29%5E2%29%29%29= %28sqrt%28+49%29%29
x-3=+-7
x=3+-7
x=3+7=10
or
x=3-7=-4
.
Solution: (10 or -4)

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2-6x-40=0 Start with the given equation


x%5E2-6x=40 Add 40 to both sides


Take half of the x coefficient -6 to get -3 (ie -6%2F2=-3)
Now square -3 to get 9 (ie %28-3%29%5E2=9)



x%5E2-6x%2B9=40%2B9 Add this result (9) to both sides. Now the expression x%5E2-6x%2B9 is a perfect square trinomial.




%28x-3%29%5E2=40%2B9 Factor x%5E2-6x%2B9 into %28x-3%29%5E2 (note: if you need help with factoring, check out this solver)



%28x-3%29%5E2=49 Combine like terms on the right side

x-3=0%2B-sqrt%2849%29 Take the square root of both sides

x=3%2B-sqrt%2849%29 Add 3 to both sides to isolate x.

So the expression breaks down to
x=3%2Bsqrt%2849%29 or x=3-sqrt%2849%29


x=3%2B7 or x=3-7 Take the square root of 49 to get 7


x=10 or x=-4 Now combine like terms

So our answer is
x=10 or x=-4


Here is visual proof

+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E2-6x-40%29+ graph of y=x%5E2-6x-40

Here we can see that the x-intercepts are x=10 and x=-4, so this verifies our answer.

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Answer:
So the answer is A)