Question 89282: Solve by completing the square.
x^2 – 16x + 63 = 0
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! Given:
.
x^2 – 16x + 63 = 0
.
Solve by completing the square.
.
The first thing to do in completing the square is to make sure that the multiplier of the
x^2 term is 1. If it is not 1, then divide the entire equation (all terms on both sides) by
the multiplier of the x^2 term. In this problem, the multiplier is 1 (it is 1*x^2)
so you don't need to do anything to change it.
.
Next, I like to get rid of the constant term on the left side. In this problem you can do that
by subtracting 63 from both sides. When you do that, the problem becomes:
.
x^2 - 16x = -63
.
Next look at the multiplier of the x term, divide it by 2, and square that result.
Then add that number to both sides of the equation. In this problem, the multiplier
of the x term is -16. Divide it by 2 and you get -8. Square the -8 and you get + 64. Add
+64 to both sides of the equation and it becomes:
.
x^2 - 16x + 64 = +1
.
The left side of this equation can be factored because it is a perfect square. When you
factor it, the number part of the factor is half of the multiplier of the x term, in
this case half of -16 which is -8. So the equation factors to:
.
(x - 8)^2 = 1
.
Take the square root of both sides and you get:
.
x - 8 = ± 1
.
Finally, add +8 to both sides to get rid of the -8 on the left side:
.
x = 8 ± 1
.
So the two answers to this problem are x = 8 + 1 = 9 and x = 8 - 1 = 7.
.
These two answers (x = 9 and x = 7) are what you were looking to find.
.
You can check them out by multiplying (x - 9) times (x - 7) and make sure the result is
the same as the original equation you were given.
.
Hope this process helps you to understand the process.
.
|
|
|
