complete the square
2x^2-4x-1=0
solve by completing the square ??
first divide by 2 and move the constant to the right ...
x^2 - 2x = 1
add 1 to both sides
x^2 - 2x + 1 = 1 + 1
(x-1)^2 = 2
x-1 = ± √2
x = 1 ± √2
To complete the square, follow these steps:
Step 1: Move the constant term to the other side of the equation.
2x^2 - 4x = 1
Step 2: Divide the coefficient of x^2 by 2 and square it. Add this value to both sides of the equation.
2x^2 - 4x + (-4/2)^2 = 1 + (-4/2)^2
2x^2 - 4x + 4 = 1 + 4
2x^2 - 4x + 4 = 5
Step 3: Rewrite the left side of the equation as a perfect square trinomial.
2(x^2 - 2x + 2) = 5
Step 4: Divide both sides of the equation by the coefficient of x^2, which is 2.
x^2 - 2x + 2 = 5/2
Now you have completed the square.