Square root property: solve (x - 1/2)^2 = 1

Stine

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Solve (x - 1/2)^2 = 1

The left-hand side is: (x - 1/2)(x - 1/2)

But what next? Can I get some direction, please? I am not sure how to do this at all. Thank you!
 

tkhunny

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Since we're playing with square roots, simply recognize that there are TWO values that, when squared, result in the same positive value.

2^2 = 4

(-2)^2 = 4

In your case:

1^2 = 1

(-1)^2 = 1

So, there are two results for 'x - 1/2'

x - 1/2 = 1 or x - 1/2 = -1

Solve each for 'x'.
 

Stine

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Ok so I solved for x = 1.5 or x=1/2

Thank you for your help tkhunny! You are just slendid! :lol:
 

tkhunny

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You may wish to check that second one.
 

Denis

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If you don't believe TK (since you called him "slendid"!), you can go the long way:
(x - 1/2)^2 = 1

x^2 - x + 1/4 = 1

x^2 - x - 3/4 = 0

4x^2 - 4x - 3 = 0

(2x - 3)(2x + 1) = 0
x = 3/2 or x = -1/2

Oh oh: he's right; better call him "splendid" :wink:
 

Stine

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OK Denis... :? you just confused me... Are you trying to say this is the long way of this answer?
 

Stine

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I mean the long way to get to the answer of this question?
 

tkhunny

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No need to be confused. That is exactly how I would have done it if you had not specifically entitled your post as you did. Solving quadratic equations should not be confusing, since there is ALWAYS a way to solve them - and rather simply at that. However, when there is an even easier way, it might be wise to use that easier way.

Normally, one would "Complete the Square" to solve such a thing. (Or use the general completed square known as the Quadratic Formula). In your problem, the square is already completed, so why undo it?
 
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