I've recently come across quadratic equations which involve brackets. I don't need answers alone but a method as what good is answers if you cannot learn and replicate?
1. (x + 3)^2 - 3 = 13
and
2. (x - 3)^2 = 25
For question 1 the answer is x = 1 or x = -7 and on question 2 the answer is x = 8 or x = -2.
I will show you the method i've used for both questions and i would appreciate your comments on what i'm doing wrong. Do i use linear equation rules to swap over the - or + to the suitable side?
1. The -3 goes over to the right hand side where 13 is so being 13+3 which gives 16 and then squareing the 16 and then because of this the square is cancelled. The equation is now (x + 3) = 4. I'm not sure why you do this but +3 + 4 = 7 and +3 - 4 = -1. So x = 7 or x = -1
For question 2 the 25 is squared thus giving (x - 3) = 5. Becuase of this -3 + 5 =2 and -3 - 5 = -8. Thus x = 2 or x = -8.
All comments are very much appreciated. Many thanks!
Quadratic Equations?
2008-07-06 12:56 pm
回答 (7)
2008-07-06 1:02 pm
✔ 最佳答案
Yeah You Are On Right Track Just Carry on
2008-07-06 8:02 pm
you're on it!
except when you square root there are two soltions
ie. x² = 9
x = ±3
except when you square root there are two soltions
ie. x² = 9
x = ±3
2008-07-07 2:11 am
Question 1
(x + 3)² = 16
x + 3 = ± 4
x = 1 , x = - 7
Question 2
(x - 3) = ± 5
x = 8 , x = - 2
(x + 3)² = 16
x + 3 = ± 4
x = 1 , x = - 7
Question 2
(x - 3) = ± 5
x = 8 , x = - 2
2008-07-06 8:31 pm
1)
(x + 3)^2 - 3 = 13
(x + 3)^2 = 13 + 3
(x + 3)^2 = 16
x + 3 = 屉16
x + 3 = ±4
x + 3 = 4
x = 4 - 3
x = 1
x + 3 = -4
x = -4 - 3
x = -7
â´ x = -7 , 1
= = = = = = = =
2)
(x - 3)^2 = 25
x - 3 = 屉25
x - 3 = ±5
x - 3 = 5
x = 5 + 3
x = 8
x - 3 = -5
x = -5 + 3
x = -2
â´ x = -2 , 8
(x + 3)^2 - 3 = 13
(x + 3)^2 = 13 + 3
(x + 3)^2 = 16
x + 3 = 屉16
x + 3 = ±4
x + 3 = 4
x = 4 - 3
x = 1
x + 3 = -4
x = -4 - 3
x = -7
â´ x = -7 , 1
= = = = = = = =
2)
(x - 3)^2 = 25
x - 3 = 屉25
x - 3 = ±5
x - 3 = 5
x = 5 + 3
x = 8
x - 3 = -5
x = -5 + 3
x = -2
â´ x = -2 , 8
2008-07-06 8:24 pm
There are not two solutions to both problems. There is only one solution for each.
For the first problem, at the end, where you say, "I'm not sure why you do this but +3 + 4 = 7..." is where your error is. If the equation is now (x+3)=4, you cannot add three to both sides, you must SUBTRACT it. Since you want to get rid of the three on the left side, you must do the opposite (it's being added to x, so you must subtract it), and you also do the same thing on the other side (subtract three from four).
So the answer is x = 1.
On number two, you made the same mistake. Once you have (x-3)=5, you can only add three to both sides to get x by itself. The answer is x=8. If you subtract three from both sides, you get x-6=2, which also ends up equaling x=8 if you add six to both sides.
For the first problem, at the end, where you say, "I'm not sure why you do this but +3 + 4 = 7..." is where your error is. If the equation is now (x+3)=4, you cannot add three to both sides, you must SUBTRACT it. Since you want to get rid of the three on the left side, you must do the opposite (it's being added to x, so you must subtract it), and you also do the same thing on the other side (subtract three from four).
So the answer is x = 1.
On number two, you made the same mistake. Once you have (x-3)=5, you can only add three to both sides to get x by itself. The answer is x=8. If you subtract three from both sides, you get x-6=2, which also ends up equaling x=8 if you add six to both sides.
2008-07-06 8:12 pm
(x + 3)^2 - 3 = 13
(x + 3)^2 = 16
x^2 + 6x + 9 - 16 = 0
x^2 + 6x - 8 = 0
(x + 7)(x - 1) = 0
x = -7 or = 1
(x - 3)^2 = 25
x^2 - 6x + 9 -25 = 0
x^2 - 6x - 16 = 0
(x - 8)(x + 2) = 0
x = 8 or x = -2
(x + 3)^2 = 16
x^2 + 6x + 9 - 16 = 0
x^2 + 6x - 8 = 0
(x + 7)(x - 1) = 0
x = -7 or = 1
(x - 3)^2 = 25
x^2 - 6x + 9 -25 = 0
x^2 - 6x - 16 = 0
(x - 8)(x + 2) = 0
x = 8 or x = -2
2008-07-06 8:05 pm
(x + 3)^2 - 3 = 13
Expand
x² + 6x + 9 - 3 = 13
Combine terms
x² + 6x - 7 = 0
(x + 7)(x - 1) = 0
x = -7, 1
(x - 3)^2 = 25
Expand
x² - 6x + 9 = 25
Combine
x² - 6x - 16 = 0
(x - 8)(x + 2) = 0
x = 8, -2
.
Expand
x² + 6x + 9 - 3 = 13
Combine terms
x² + 6x - 7 = 0
(x + 7)(x - 1) = 0
x = -7, 1
(x - 3)^2 = 25
Expand
x² - 6x + 9 = 25
Combine
x² - 6x - 16 = 0
(x - 8)(x + 2) = 0
x = 8, -2
.
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