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Quadratic Equation

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by wtpooh » Tue Apr 18, 2006 6:39 pm
I am trying to understand the underlying solution to this problem taken from Manhattan GMAT.

Find t :

t2(t-square)+2t+1=18

Since the equation cannot be factored easily, one can utilize a formula to derive t.

But MGmat solves the equation by:
(t+1)(t+1) = square root of 18...

culminating in a positive and negative t.

Question is : why square root the integer 18?
And why a positive and negative answer?
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by chix475ntu » Wed Apr 19, 2006 9:04 am
Positive and negative - because when you square a positive or negative number, the result will be positive. So the root of a positive number can be positive or a negative numbers

EX: -2 ^ 2 = 4 and 2^ 2 = 4 .. so the sq root 4 = +- 2
HTH
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by wtpooh » Wed Apr 19, 2006 5:00 pm
Right.. Then, why square root of 18?
Is that a rule?

The equation is equal to 18..
You break down the equation into (t+1)(t+1)...
and all of the sudden, the equation is equal to square root of 18...
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by beatthegmat » Wed Apr 19, 2006 9:14 pm
(t +1)^2 = (t + 1)(t +1) = 18

Thus the square root of (t + 1)^2 = (t + 1) = square root of 18

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by wtpooh » Thu Apr 20, 2006 8:57 pm
Thanks. You are right.
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by naveen1003 » Thu Jun 09, 2011 1:03 am
Find t :
t2(t-square)+2t+1=18
t^2 + 2t + 1 = (t+1)^2 = 18
(t+1) = ± √18
t = -1 ± √18
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