by completing the square method solve the equation.
x^2-2x-1
can u factor it? when i did it it couldn't be factored. i also don't know why it is not factorable because its a perfect square right?
please help me
Answered below.
To solve the equation by completing the square method, follow these steps:
Step 1: Move the constant term (-1) to the right side of the equation:
x^2 - 2x = 1
Step 2: Divide the coefficient of the x term by 2, square the result, and add it to both sides of the equation:
x^2 - 2x + (-2/2)^2 = 1 + (-2/2)^2
x^2 - 2x + 1 = 2
Step 3: Factor the left side of the equation as a perfect square:
(x - 1)^2 = 2
Step 4: Take the square root of both sides and solve for x:
x - 1 = ±√2
x = 1 ± √2
So the solutions to the equation x^2 - 2x - 1 = 0 are x = 1 + √2 and x = 1 - √2.
Now, addressing your question about factoring, the equation x^2 - 2x - 1 cannot be factored using simple integer coefficients because it does not have rational roots. Despite being a quadratic, it is not a perfect square. However, the equation can still be solved using the completing the square method or other methods such as the quadratic formula.