Problem #1
Solve by completing the square
2x^2-4x-11=0
My answer: x = (2+/-sqrt 26)/(2)
Problem #2
Solve by using the quadratic formula
x^2-4x-60=0
My answer: x = (2+/-sqrt 16)/(2)
You did not do it completeing the square. Please show work.
ON the second b^2-4ac is 16+240. How did you get 16 out of that?
To solve Problem #1 by completing the square, follow these steps:
Step 1: Move the constant term to the right side of the equation:
2x^2 - 4x = 11.
Step 2: Divide the entire equation by the coefficient of x^2 to make the coefficient 1:
x^2 - 2x = 11/2.
Step 3: Take half of the coefficient of x, square it, and add it to both sides of the equation:
x^2 - 2x + (2/2)^2 = 11/2 + (2/2)^2.
x^2 - 2x + 1 = 11/2 + 1.
Simplifying the equation:
x^2 - 2x + 1 = 14/2.
Step 4: Factor the left side of the equation as a perfect square trinomial:
(x - 1)^2 = 14/2.
Step 5: Take the square root of both sides of the equation:
√[(x - 1)^2] = √(14/2).
Take note that the square root introduces a positive and negative root on the right side:
x - 1 = ±√(14/2).
Step 6: Solve for x by adding 1 to both sides of the equation:
x = 1 ± √(14/2).
Simplifying the square root:
x = 1 ± √(7).
This is the correct solution for Problem #1 by completing the square.