3x^2-4x-5
Divide 3 out.
x^2-4x/3-5/3
Now here's where I'm confused. Am I supposed to just divide the coefficient by 2, or am I supposed to divide the fraction by 2? It's either -4x/2 which turns into -2x/3 or divide the fraction by two which is -4x/3 * 2/1.
Completing the square?
2009-02-08 4:52 pm
回答 (6)
2009-02-08 5:23 pm
✔ 最佳答案
3x^2-4x-5=0x^2-4/3x-5/3=0.....we get square of [(-4/3)/2]^2=4/9
x^2-4/3x=5/3...........add 4/9 both sides of the equation
x^2-4/3x+4/9=5/3+4/9
(x-2/3)^2=19/9
x-2/3=+/-√(19/9)
x=2/3+/-√(19)/3
.....2+√(19)......2.-√(19)
x=--------------- ,-------------- answer//
..........3..............3.........
2009-02-08 7:13 pm
3 [ x ² - (4/3) x ] - 5
3 [ x ² - (4/3) x + 4/9 ] - 5 - 4/3
3 (x - 2/3) ² - 19/3
3 [ x ² - (4/3) x + 4/9 ] - 5 - 4/3
3 (x - 2/3) ² - 19/3
2009-02-08 5:14 pm
Using "complete the square" the first tern needs to be square, so multiply everything by 3.
9x^2 -12x -15 = 0
move -15 to right side
9x^2 -12X = 15
add 4 to complete the square
9x^2 - 12x +4 =19
(3x -2)(3x -2) =19
3x-2 = =/- sqrt(19)
x = (2 +/1sqrt(19))/3
x = 2.120 or x= -.78
9x^2 -12x -15 = 0
move -15 to right side
9x^2 -12X = 15
add 4 to complete the square
9x^2 - 12x +4 =19
(3x -2)(3x -2) =19
3x-2 = =/- sqrt(19)
x = (2 +/1sqrt(19))/3
x = 2.120 or x= -.78
2009-02-08 5:06 pm
3x^2 - 4x - 5
= (3x^2 - 4x - 5)/3
= x^2 - 4x/3 - 5/3
= x^2 - 2x/3 - 2x/3 - 5/3
= x^2 - 2x/3 - 2x/3 + 4/9 - 5/3 - 4/9
= (x^2 - 2x/3) - (2x/3 - 4/9) - 15/9 - 4/9
= x(x - 2/3) - 2/3(x - 2/3) - 19/9
= (x - 2/3)(x - 2/3) - 19/9
= (x - 2/3)^2 - 19/9
= (3x^2 - 4x - 5)/3
= x^2 - 4x/3 - 5/3
= x^2 - 2x/3 - 2x/3 - 5/3
= x^2 - 2x/3 - 2x/3 + 4/9 - 5/3 - 4/9
= (x^2 - 2x/3) - (2x/3 - 4/9) - 15/9 - 4/9
= x(x - 2/3) - 2/3(x - 2/3) - 19/9
= (x - 2/3)(x - 2/3) - 19/9
= (x - 2/3)^2 - 19/9
2009-02-08 4:59 pm
-4/3 divided by two is -4/2*3 = -4/6 = -2/3
2009-02-08 4:57 pm
-4/3:2=-4/3*1/2=-4/6
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