You can
put this solution on YOUR website!1/2x2 + 1/3x - 6 = 4
1. Divide through by the coefficient of x2
This is 1/2. To divide by 1/2 is to multiply through by 2
2(1/2x2) + 2(1/3x) - 2(6) = 2(4)
x2 + 2/3x - 12 = 8
2. Get rid of the constant term on the left by adding its opposite
to both sides:
x2 + 2/3x = 8 + 12
x2 + 2/3x = 20
3. Find the square-completing number by
(a) multiplying the coefficient of x by 1/2
(2/3)·(1/2) = 1/3
(b) squaring this result
(1/3)2 = 1/9
4. Add the square-completing number to both sides
x2 + 2/3x + 1/9 = 20 + 1/9
5. Factor the left side, and if everything is done right,
it will factor into two equal factors, which is a
perfect square:
(x + 1/3)(x + 1/3) = 20 + 1/9
(x + 1/3)2 = 20
6. Combine the terms on the right
(x + 1/3)2 = 180/9 + 1/9
(x + 1/3)2 = 181/9
6. Take the square roots of both sides, remembering to put ± on the
right:
_____
x + 1/3 = ±V181/9
5. Solve for x:
_____
x = =1/3 ± Ö181/9
6. Simplify the radical:
The numerator, 181, is a prime number, so we leave it under the
radical. We take the square root of the denominator, 9, and get 3
___
x = -1/3 ± Ö181/3
If you like you may write this as a single fraction with denomninator 3
___
x = (-1 ± Ö181)/3
Edwin
AnlytcPhil@aol.com
