13. x2+ 4x - 12 = 0
17. x2 + 3x - 27 = 0
29. 2x2 - 4x + 1 = 0
31. 4x2 - 2x - 1 = 0
2007-04-29 07:01:41 · 6 answers · asked by Dave 4 in Science & Mathematics ➔ Mathematics
Completing the square
x² + 4x - 12 = 0
x² + 4x - 12 + 12 = 0 + 12
x² + 4x = 12
x² + 4x + ______ = 12 + _____
x² + 4x + 4 = 12 + 4
(x + 2)(x + 2) = 16
(x + 2)² = 16
(√x + 2)² = ± √16
x + 2 = ± 4
x + 2 - 2 = - 2 ± 4
x = - 2 ± 4
- - - - - - - - - - -
Solving for +
x = - 1 + 4
x = 3
- - - - - - - - -
Solving for -
x = - 2 - 4
x = - 6
- - - - - - - - s-
2007-04-29 07:40:19 · answer #1 · answered by SAMUEL D 7 · 1⤊ 0⤋
winding up the sq. is effectual in circumstances like this that have not have been given a speedy factoring answer. right this is the 1st one. x^2 - 6x - 3 = 0. the 1st step is to isolate the x words and the constants. So, right here, upload 3 to the two factors. x^2 - 6x = 3. Now, to end the sq., we upload to the two factors the quantity which will enable us to element the left element in to a style of (ax + b)^2. This quantity is (6/2)^2. Why? We could desire to be waiting to characteristic b to itself to get 6. In different words, 2b = 6. So, our equation turns into: x^2 - 6x + (6/2)^2 = 3 + (6/2)^2. Simplifying supplies us: x^2 - 6x + 9 = 12 (x - 3)^2 = 12 x - 3 = +/- sqrt(12) x = 3 +/- 2(sqrt(3)). the 2nd comprises one better step by using first term being superior via 2. Set it up as follows. 2x^2 + 10x + 11 = 0 2x^2 + 10x = (-11) x^2 + 5x = (-5.5) or (-11/2). Then, save on with the technique centred above. x^2 + 5x + (5/2)^2 = (-11/2) + (5/2)^2 x^2 + 5x + 25/4 = (-22/4) + (25/4) (x + (5/2))^2 = 3/4 x + 5/2 = +/- (sqrt(3))/2 x = (-5/2) +/- (sqrt(3))/2 = (-5 +/- sqrt(3))/2.
2016-10-14 02:27:48 · answer #2 · answered by ? 4 · 0⤊ 0⤋
The way is as follows:
1) Take the coeffecient of x^2 as a common factor from the terms containing x^2 & x
ex. 2 (x^2 - 2x ) +1
2) Add and subtract the sqaur of 1/2 the coeffecient of x
i.e. 2( x^2 - 2x +1 -1 )+1
3) write the complet square U get
i.e. 2(x-1)^2 -2 +1 = 0
2(x-1)^2= 1
(x -1)^2 = 1/2
x-1= +/- sqrt(2)/2
x = 1 +/- sqrt(2)/2
2007-04-29 07:41:17 · answer #3 · answered by a_ebnlhaitham 6 · 0⤊ 0⤋
number 17 and 31 requires that qudractic equation
2007-04-29 07:12:10 · answer #4 · answered by Mike 4 · 0⤊ 0⤋
meh, why not; I'm bored
13. (x+6)(x-2)
29. (2x-1)(2x-1)
the others I can't figure out
2007-04-29 07:08:33 · answer #5 · answered by Anonymous · 0⤊ 0⤋
Do it yourself.
Looking at your asked questions, you have a long history of asking everyone to do your math hw for you, maybe thats why u get such bad grades.
2007-04-29 07:03:49 · answer #6 · answered by I am watching your every move. 3 · 0⤊ 1⤋