SOLUTION: Choose the one alternative that best completes the statement or answers the question. Solve by completing the square. x^2 - 6x

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

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)   (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
================
Cheers,
Stan H.
Answer by tutorcecilia(2152)   (Show Source): You can put this solution on YOUR website!
x^2 - 6x - 40+40 =40
x^2-6x=40
}=

=
=
=49
=49 [factor]
= 49
=
x-3=+-7
x=3+-7
x=3+7=10
or
x=3-7=-4
.
Solution: (10 or -4)

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

Start with the given equation

Add 40 to both sides

Take half of the x coefficient -6 to get -3 (ie )
Now square -3 to get 9 (ie )

Add this result (9) to both sides. Now the expression is a perfect square trinomial.

Factor into (note: if you need help with factoring, check out this solver)

Combine like terms on the right side

Take the square root of both sides

Add 3 to both sides to isolate x.

So the expression breaks down to
or

or Take the square root of 49 to get 7

or Now combine like terms

So our answer is
or

Here is visual proof

graph of

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

=========================================
Answer:
So the answer is A)
RELATED QUESTIONS
Choose the one alternative that best completes the statement or answers the question.... (answered by stanbon)
Write the word or phrase that best completes each statement or answers the question. The (answered by rajagopalan)
Choose the one alternative that best completes the statement or answers the question. (answered by Jk22)
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the... (answered by stanbon)
Determine the center, vertices, and foci for the following ellipse... (answered by MathLover1,KMST)
Short answer. Write the word or phrase that best completes each statement or answers the... (answered by stanbon,Annie C)
Select the numeral preceding the expression that best answers the question or completes... (answered by LinnW,Edwin McCravy)
Write the word or phrase that best completes each statement or answers the following... (answered by richwmiller)
Solve by completing the square. Leave answers in radical form. Thank you -2x + 6 =... (answered by MathLover1)