What number is used to complete the square for the equation x^2 = 20x?
a) 100
b) 10
c) -10
d) -100
a
Yes again.
x^2 -10x + 100 = 100
(x -10)^2 = 100
x -10 = +/- 10
x = 0 or 20
The same answer could have been obtained by factoring
x(x-20) = 0
no, when you plug 100 in to check, you get 10,000=2,000...plug in the other numbers and try them
To complete the square for the equation x^2 = 20x, you need to find a number that, when added to both sides of the equation, creates a perfect square on the left side.
Here's how you can find the number:
1. Start with the equation: x^2 = 20x.
2. Divide both sides of the equation by 2: x^2/2 = 20x/2.
This simplifies the equation to: x^2/2 = 10x.
3. Take half of the coefficient of x (which is 10) and square it: (10/2)^2 = 5^2 = 25.
This gives you the number you need to complete the square.
4. Add the number (25) to both sides of the equation: x^2/2 + 25 = 10x + 25.
The left side becomes a perfect square: (x/√2)^2 + 25 = 10x + 25.
5. Simplify the equation: (x/√2)^2 = 10x.
6. Now, we can see that the number used to complete the square is 25.
Therefore, the correct answer is a) 100.
So, to complete the square for the equation x^2 = 20x, the number used is 100.