x^2 - 4x + 4 = 0
Find the roots by completing the square
I got {2,2}. Is this correct?
yes 2 is the solution
To find the roots of the quadratic equation x^2 - 4x + 4 = 0 using the method of completing the square, follow these steps:
1. Make sure the equation is in the form: x^2 + bx + c = 0. In this case, the equation is already in that form.
2. Take half of the coefficient of the x-term (-4x) and square it. Half of -4 is -2, and -2 squared is 4. So, we need to add 4 to both sides of the equation to maintain balance.
x^2 - 4x + 4 + 4 = 0 + 4
Simplifying, we get: x^2 - 4x + 8 = 4
3. Rewrite the left side of the equation as a perfect square trinomial. In this case, the trinomial is (x - 2)^2.
(x - 2)^2 = 4
4. Take the square root of both sides of the equation.
√((x - 2)^2) = ±√4
Simplifying, we get: x - 2 = ±2
5. Solve for x by adding 2 to both sides of the equation.
x - 2 + 2 = 2 ± 2
Simplifying, we get: x = 2 ± 2
So the solutions are x = 2 + 2 = 4 and x = 2 - 2 = 0.
Therefore, the roots of the quadratic equation x^2 - 4x + 4 = 0 after completing the square are {4, 0}.
Hence, your answer {2, 2} is not correct.