Help me solve: A table for y = x^2 - 25 is given below. Solve each equation or inequality. x = -6, -5, -1, 0, 1, 5, 6 y = 11, 0, -24, -25, -24, 0, 11 a.) x^2 - 25 = 0 b.) x^2 - 25 0

Question

Help me solve:
A table for y = x^2 - 25 is given below. Solve each equation or inequality.

x = -6, -5, -1, 0, 1, 5, 6
y = 11, 0, -24, -25, -24, 0, 11

a.) x^2 - 25 = 0
b.) x^2 - 25 < 0
c.) x^2 - 25 > 0

e.mccormick · Answer

Difference of squares, a stock equation, is what Luis popped in with, which is a good thing to remember!

e.mccormick · Answer

Take any two squares, like the $x^2$ and $b^2$ that he used, and their difference is always going to come out like that.
$x^2-b^2=(x-b)(x+b)$

anonymous · Answer

Use difference of squares:$$(x^2-y^2)=(x-y)(x+y) \implies x^2-25 = (x-..)(x+..)$$Can you tell us what the expression turns in to now?

@angelina22309

anonymous · Answer

Am I just suppose to plug in one of the x values it gives me?

e.mccormick · Answer

So what part of this one was giving you trouble?

e.mccormick · Answer

Ah, so they do not tell you what needs to be done in this one?

anonymous · Answer

Solve each equation or inequality

e.mccormick · Answer

AH.  OK.  Also, look at b and c, you put them in as the same.

e.mccormick · Answer

OK.  So we have a), the $x=\{-5,5\}$ and $y=0$.  At this point, I think this is asking you to account for al the numbers below, but not 100% sure.  However, from finding that first thing you can work towards the others.

anonymous · Answer

I updated the question @e.mccormick

e.mccormick · Answer

OK.  this looks like they want you to make it into a set of equations for when one thing or another is true.

anonymous · Answer

|dw:1365978636379:dw|
Does this make sense?

@angelina22309