Quadratic Equation

[wtpooh]

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?

[chix475ntu]

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

[wtpooh]

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...

[beatthegmat]

(t +1)^2 = (t + 1)(t +1) = 18

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

Is this what you are asking about?

[wtpooh]

Thanks. You are right.

[naveen1003]

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

t^2 + 2t + 1 = (t+1)^2 = 18
(t+1) = ± √18
t = -1 ± √18