please assist me in:
1. solve by completing the square. p2 - 8p = 0.
p2 - 8p = 0
Multiply the coefficient of p, which is -8 by 1/2.
That gives -4. Square -4. That gives +16. Add 16
to both sides of the equation:
p2 - 8p + 16 = 0 + 16
Factor the left side. The right side is just 16
(p - 4)(p - 4) = 16
The left side can be written (p - 4)2
(p - 4)2 = 16
Use the principle of square roots:
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p - 4 = ±Ö16
16 is the square of 4, so 4 is the positive square root of 16
p - 4 = ±4
Add 4 to both sides:
p = 4 ± 4
Using the +, p = 4 + 4 = 8
Using the -, p = 4 - 4 = 0
The solutions are 8 and 0.
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2. solve by graphing x2 + 6x - 2 = 0
Write this as the system of equations by
letting y = the left side and y = the right side:
y = x2 + 6x - 2
y = 0
Graph each of these by getting some points on each
y = x2 + 6x - 2
Some points are (-7,5), (-6,-2), (-5,-7), (-4,-10),
(-3, -11), (-2,-10), (-1,-7), (0,-2), (1,5)
Plotting these:
Now draw a smooth curve through all those points:
Now we draw the equation of y = 0, but this is just the x-axis
so we want to find the points where the curve crosses the x-axis.
The best we can do is estimate what we think these points are.
I'll mark these on the x-axis and what I think they are:
I "guess"-timate that the one on the right is about
1/3 of the way between 0 and 1, so I'll call it .3.
I slso "guess"-timate that the one on the left is about
1/3 of the way between -6 and -7, so I'll call it -6.3.
Edwin
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