Solve by completing the square.
1. x(squared)-6x=7
2. x(squared)+14x-9=6
2007-05-02 15:41:25 · 6 answers · asked by TracyM 1 in Science & Mathematics ➔ Mathematics
1. x^2 -6x =7
You look at the coefficient of the x term, which in this case is -6. You take half of that, which is -3. You square that, which is 9. You add the 9 to both sides of the equation:
x^2-6x+9=7+9
x^2-6x+9=16
Then, you can factor the left side into a square:
(x-3)(x-3)=16
(x-3)^2 = 16.
Then you square root both sides:
x-3= 4 or -4
x=3+4 or 3-4
x= 7 or -1
Check them : 49-42=7 and 1+6=7.
2. I would add that 9 to the other side first to get
x^2+14x=15
Then just like #1, take half of 14, square it, add to both sides. Try it yourself, you can do it!
2007-05-02 15:56:13 · answer #1 · answered by Anonymous · 0⤊ 0⤋
Please use the carat (^) to denote a power.
Completing a square:
x^2- 6x = 7
Now if I had x^2 -6x + 9, I'd have a perfect square (x-3)^2. By adding 9 to both sides of the eqtn, I have this form; Then (x-3)^2 = 7+9 = 16
Taking the square root (x-3) = +/- 4
So x=7 and -1
x^2 + 14 x - 9 = 6 or x^2 +14 x = 15.
Same deal. x^2+14x+49 is a perfect square, so I have add 49 to both sides to get
(x+7)^2 = 64
Take the square root and x+7 = +/- 8
Then x= -15 or 1
2007-05-02 15:52:03 · answer #2 · answered by cattbarf 7 · 0⤊ 0⤋
1. take 1/2 of -6 and get -3 and then square it and get 9. Now add 9 to both sides of the equation.
x^2 -6x +9 =16
factor
(x-3)^2 = 16
take the square root
x-3 = plus or minus 4
x-3 = 4, x = 7 or
x-3 =-4, x = -1
2. add 9 to both sides and get
x^2 +14x = 15
take 1/2 of 14 and get 7 and then square it and get 49 and add that amount to both sides.
x^2 +14x +49 = 15 + 49
x^2 + 14x +49 = 64
factor
(x+7)^2 =64
square root both sides
x+7 = plus or minus 8
x+7 = 8, x =1
or
x+7 = -8, x = -15
2007-05-02 15:52:42 · answer #3 · answered by lizzie 3 · 0⤊ 0⤋
(1) x^2-6x=7
x^2-6x+9=7+9=16
(x-3)^2=16
x-3=4
x=7
(2)x^2+14x-9=6
x^2+14x=15
x^2+14x+49=15+49=64
(x+7)^2=64
x+7=8
x=1
2007-05-02 15:51:58 · answer #4 · answered by Joe M 1 · 0⤊ 0⤋
1.
x^2 - 6x = 7
x^2 - 6x +9 = 7+9
(x-3)^2 = 16
x-3 = 4
x = 7
Or
-(x-3) = 4
- x +3 = 4
-1 = x
2.
x^2+14x-9=6
x^2+14x+49 = 6+58
x^2 +14x+49 = 64
(x+7)^2 = 8^2
x+7=8
x=1
or
-(x+7) = 8
-x -7 = 8
x = -15
2007-05-02 15:50:39 · answer #5 · answered by Steve A 7 · 0⤊ 0⤋
(x+1)(x-7)
(x+15)(x-1)
2007-05-02 15:51:17 · answer #6 · answered by Anonymous · 0⤊ 0⤋