What are two numbers which multiply to make #-9450# and add to make #-15# ?

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Nimo N. Share
Jun 6, 2018

Answer:

The question was changed after posting my original answer... I re-worked the problem and obtained two possible combinations.

Explanation:

"two numbers add to make -15" gives equation 1):
1) # A + B = -15 #
"two numbers multiply to make -9450", gives:
2) # AB = -9450 #

Solve equation 1) for A, then substitute into equation 2), to get B.
1a) # A = -15 - B #
# (-15 - B)B = -9450 #
Multiply, then add 9450 to both sides, to get,
# -15B - B^2 + 9450 = 0 #
# -B^2 - 15B + 9450 = 0 #
Use the quadratic formula.
# B = ( -(-15) +- sqrt( (-15)^2 - 4 (-1) (9450) ) )/(2(-1)) #
# B = ( 15 +- sqrt( 225 + 37800 ) )/(-2) #

# B = ( 15 +- sqrt( 38025 ) )/(-2) #

# B_("using" -) = ( 15 - sqrt( 38025 ) )/(-2) #
# B_("using" -) = 90 #
# ----- #

# B_("using" +) = ( 15 + sqrt( 37825 ) )/(-2) #
# B_("using" +) = ( -15 - 5 sqrt( 1513 ) )/(2) #, Exact.
# B_("using" +) = -104.74 #, Approximate.
# ----- #

Substitute into 1a) to obtain two possible (approximate) values for A.
# A = -15 - (90) #
# A = -105 #

# A = -15 - (-104.74) #
# A = 89.74 #

There are two possible combinations of numbers for A and B:
( -105, 90)
(89.74, -104.74 )

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Write your answer here...
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Answer

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Answer:

Explanation

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Jun 6, 2018

Answer:

#-105 xx 90 = -9450#

#-105 +90 = -15#

Explanation:

One number has to be positive and one has to be negative to give a negative product.

Factors which differ by #15# are close to the square root of a number. They will be about #7# bigger or smaller than the square root.

#sqrt 9450 =97.211...#

Try numbers less than #97#

#9450 div 95 = 99.47" "larr# does not work
#9450 div 94 = 100.53" "larr# does not work
#9450 div 90 = 105" "larr# These are the factors

#-105 xx 90 = -9450#

#-105 +90 = -15#

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