lizzy87
How to solve X^2+10x=24 by completing the square.



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earslan100
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what times what equals 24 and those same numbers have to add upto 10

earslan100
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12 and 2 right?

znimon
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or 4 and 6

henpen
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\[x^2+10x=(x+5)^225\]
Do you understand this?

earslan100
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no 4 and 6 when u multiply its 24 not 24

earslan100
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srry it has to multiply to 24

henpen
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... or we could actually help him with the mechanics of the question

henpen
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*or her

earslan100
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so the answer is (x2)(x+10)

earslan100
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if you multiply using foils u can see it equals the question

henpen
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Really, that's not completing the square.


earslan100
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okie

earslan100
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ur right srry

henpen
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Okay, @lizzy87 , do you understand why\[x^2+10x=(x+5)^225\]?

lizzy87
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how didi you get the 5?

henpen
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dw:1346521462011:dw
Because 2x5=10

henpen
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dw:1346521508364:dw

henpen
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And if you take away 25 and cancel the 2 5x's into one 10x, that happens.

henpen
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dw:1346521563679:dw

lizzy87
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oh ok see how you got that thanks

henpen
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\[x^2+10x=24\]
\[x^2+10x=(x+5)^225\]
Therefore\[24=(x+5)^225\] and\[49=(x+5)^2\]

henpen
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1 Did you understand that
2 What do you think we could do now to simplify?

henpen
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\[\pm \sqrt{49}=x+5\]