Question

Rewrite the equation by completing the square. 4x^2-4x+1=0

Answer 1

(x+(-x))²=0

Explanation:

4 - a

-4 - b

1 - c

D = b²-4ac

D = (-4)² - 4×4×1

D = 16-16=0 => only one root

x= -b/2a

x= 4/2×4

x= 4/8 = 1/2 = 0.5

Answer 2

The equation
`\(4x^2 - 4x + 1 = 0\)` can be rewritten as
`\((x - 1/2)^2 = 0\)`.

To rewrite the equation
`\(4x^2 - 4x + 1 = 0\)` by completing the square, follow these steps:

Step 1: Move the constant term (1) to the right side of the equation:

`\[4x^2 - 4x = -1\]`

Step 2: Factor out the coefficient of the
`\(x^2\)` term (4) from the terms containing
`\(x^2\)` and
`\(x\)`:

`\[4(x^2 - x) = -1\]`

Step 3: To complete the square for the quadratic expression inside the parentheses, we need to take half of the coefficient of the
`\(x\) term (-1/2)`, square it, and add it to both sides of the equation:

`\[4(x^2 - x + (-1/2)^2) = -1 + 4(-1/2)^2\]`

Step 4: Simplify the right side of the equation:

`\[4(x^2 - x + 1/4) = -1 + 4(1/4)\]`

`\[4(x^2 - x + 1/4) = -1 + 1\]`

`\[4(x^2 - x + 1/4) = 0\]`

Step 5: Rewrite the left side of the equation as a perfect square:

`\[4(x - 1/2)^2 = 0\]`

Now, the equation is in the form
`\((x + ?)^2 = ?\)`, and you can see that
`\(x + 1/2\)` is the term inside the square, and the right side is 0.

So, the answer is
`\((x - 1/2)^2 = 0\)`.