Reiny Thanks for your help. But you lost me. I still end up with +/- 7 How did you get 1/16 I am con fused here.
no 2 you have to take 1/2 of 3/2 which would be 3/4.
then 3/4 squared is 9/16
so line 4 should read
x^2 - (3/2)x + 9/16 = -1/2 + 9/16
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(x-3/4)^2 = 1/16 ( how did you get 1/16)
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x=1 or x=1/2
9/16- 1/2= 9/16-8/16= 1/16
I apologize for the confusion. Let's go through the steps again to clarify how we get 1/16 as the answer.
Let's start from line 4 of your equation:
x^2 - (3/2)x + 9/16 = -1/2 + 9/16
To simplify the equation, we want to isolate the squared term on one side of the equation. To do this, we can rewrite the constant term (-1/2 + 9/16) as 8/16 - 1/2, which gives us:
x^2 - (3/2)x + 9/16 = 8/16 - 1/2
Simplifying the right side of the equation, we have:
x^2 - (3/2)x + 9/16 = 8/16 - 8/16
Combining like terms, we get:
x^2 - (3/2)x + 9/16 = 0
Now, we have a quadratic equation in the form of (x - h)^2 = k, where h is the horizontal shift and k is the vertical shift.
Comparing this equation to our equation, we can see that the constant term on the right side is 0, so k = 0. Therefore, we have:
(x - h)^2 = 0
This means that the squared term (x - h)^2 will equal 0 when x = h. In our case, h = 3/4, so:
x - (3/4) = 0
Solving for x, we get:
x = 3/4
So, the equation (x - 3/4)^2 equals 0 when x = 3/4, not 1/16 as mentioned in your question.
I apologize for the mistake in my previous response. Thank you for pointing it out. I hope this clarifies the confusion.