Solve by whatever Method
1. X^2 +8X = -16
X^2 +8X +16 = -16 +16
(X +4)^2 =0
X+4 =+/- SQRT 0
X=-4+/- 0
X=-4, X=4
2. 3x^2-2x-5=0
X=-b+/- sqrt (b)^2-4ac
2a a=3 ,b=-4,c=-5
X=-(-2)+/- Sqrt (-2)^2-4(3)(-5)
2(3)
X=2+/sqrt64 = 2+/-8
6
X= 2+8=10/6=1 2/3, x=2-8=-6/6=-1
Solution set is 1 2/3, -1
Solve by completing the square
3. X^2-x-1=0
X^2-x=1
X^2-1/2x=1/2
X^2-1/2x+ (1/2)^2=1/2 +(1/2)^2
X^2x+1/4=1/2+1/4
(X-1/4)^2=1/2
X-1/4=+/1/2
x=1/2+/-1/2
x=1, x=0
Just want to see if I am on the right path. Thanks Much!!!
#1, OL
#3, look at lines 5 and 6
1/2 + 1/4 = 3/4 not 1/2, take it from there
in #2 you are guilty of "bad form"
you have X= 2+8=10/6=1 2/3, x=2-8=-6/6=-1
using the = sign means that whatever you just wrote is equal to the next part.
I see x = 2+8 = 10/6..
2+8 is not equal to 10/6, you can't just drop numbers and then bring them back
that line should have read:
x=(2+8)/6 or x =(2-8)/6
x=10/6 or x=-6/1
x=5/3 or x = -1
For problem #1, the correct solution is X = -4 and X = 4. You correctly completed the square to get (X + 4)^2 = 0, then solved for X by taking the square root of both sides and considering the positive and negative roots.
For problem #2, you made a mistake in your calculation. The correct solution is X = 5/3 and X = -1. To solve this quadratic equation, you correctly used the quadratic formula, X = (-b +/- sqrt(b^2 - 4ac)) / (2a). Plugging in the values a = 3, b = -2, and c = -5, you should have:
X = (-(-2) +/- sqrt((-2)^2 - 4 * 3 * (-5))) / (2 * 3)
X = (2 +/- sqrt(4 + 60)) / 6
X = (2 +/- sqrt(64)) / 6
X = (2 +/- 8) / 6
X = 10/6 or X = -6/6
X = 5/3 or X = -1
For problem #3, you correctly used the method of completing the square. However, you made a mistake in the calculation of (1/2) + (1/4). The correct answer is (3/4), not (1/2). Additionally, after finding that (x - 1/4)^2 = 3/4, instead of writing x = 1/2 +/- 1/2, the correct expression should be x = 1/4 +/- sqrt(3)/2. So the correct solution is x = 1/4 + sqrt(3)/2 or x = 1/4 - sqrt(3)/2, which is equivalent to x = 1 or x = 0.