SOLUTION: what two numbers multiply to equal -3136 and add up to equal 15?

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Question 828420: what two numbers multiply to equal -3136 and add up to equal 15?
Found 3 solutions by stanbon, TimothyLamb, josmiceli:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
what two numbers multiply to equal -3136 and add up to equal 15?
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Equations:
xy = -3136
x + y = 15
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Substitute for "x" and solve for "y":
(15-y)y = -3136
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y^2 - 15y - 3136 = 0
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(y-64)(y+79) = 0
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If y = 64, x = -79
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Ans: y = 79, x = -64

Answer by TimothyLamb(4379) About Me  (Show Source):
You can put this solution on YOUR website!
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xy = -3136
x + y = 15
y = 15 - x
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xy = -3136
x(15 - x) = -3136
15x - xx = -3136
-xx + 15x + 3136 = 0
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the above quadratic equation is in standard form, with a=-1, b=15, and c=3136
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to solve the quadratic equation, by using the quadratic formula, copy and paste this:
-1 15 3136
into this solver: https://sooeet.com/math/quadratic-equation-solver.php
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the quadratic has two real roots at:
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x = -49
x = 64
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answer:
x = -49
y = 64
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Solve quadratic equations, quadratic formula:
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Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+x%2Ay+=+-3136+
+x+%2B+y+=+15+
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+y+=+15+-+x+
By substitution:
+x%2A%28+15-x+%29+=+-3136+
+-x%5E2+%2B+15x+%2B+3136+=+0+
Use the quadratic formula
+x+=+%28+-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+-1+
+b+=+15+
+c+=+3136+
+x+=+%28+-15+%2B-+sqrt%28+15%5E2+-+4%2A%28-1%29%2A3136+%29%29+%2F+%282%2A%28-1%29%29+
+x+=+%28+-15+%2B-+sqrt%28+225+%2B+12544%29%29+%2F+%28-2%29+
+x+=+%28+-15+%2B-+sqrt%28+12769%29%29+%2F+%28-2%29+
+x+=+%28+-15+%2B+113+%29%2F%28-2%29+
+x+=+98%2F%28-2%29+
+x+=+-49+
and, also
+x+=+%28+-15+-+113+%29%2F%28-2%29+
+x+=+-128%2F%28-2%29+
+x+=+64+
The numbers are 64 and -49
check:
+x%2Ay+=+-3136+
+64%2A%28-49%29+=+-3136+
+-3136+=+-3136+
and
+x+%2B+y+=+15+
+64+%2B%28-49%29+=+15+
+15+=+15+
OK