Question 545970: I don't understand this problem confused it asked to solve the quadratic equation by completing the statement.
x2^-14x=-45 Found 2 solutions by ankor@dixie-net.com, Edwin McCravy:Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! solve the quadratic equation by completing the statement.
x^2 - 14x = -45
I think they may mean by "completing the square"
x^2 - 14x + ____ = -45
To complete the square, we divide the coefficient of x by 2 and square it
That would be 14/2 = 7, 7^2 = 49, so we have
x^2 - 14x + 49 = -45 + 49, we have to add 49 to both sides
x^2 - 14x + 49 = 4
Which is
(x-7)^2 = 4
Find the square root of both sides
x - 7 = +/-
x - 7 = +/- 2
Two solutions
x = 7 + 2
x = 9
and
x = 7 - 2
x = 5
x² - 14x = -45
To find out what number to add to both sides,
1. Take the coefficient of x which is -14
2. Multiply it by to get -14() = -7
3. Square that result: (-7)² = 49
4. Add that number to both sides of the equation:
x² - 14x + 49 = -45 + 49
Factor the left side, and combine the number on the right:
(x - 7)(x - 7) = 4
Write the left side as (x - 7)²
(x - 7)² = 4
Use the principle of square roots
x - 7 = ±2
Use the + Use the -
x - 7 = +2 x - 7 = -2
x = 9 x = 5
Edwin
