Step-by-step explanation:
x² − 4x = 0
To complete the square, take half of the second coefficient, square it, then add the result to both sides.
(-4/2)² = 4
x² − 4x + 4 = 4
(x − 2)² = 4
x − 2 = ±2
x = 2 ± 2
x = 0 or 4
We have rewritten the equation by completing the square as (x - 2)² -4 = 0.
This is a process in which a certain number is added and subtracted to a given equation in such a way that there is no overall effect on the equation. But the number that is added is used to complete the square using identities.
It is given that x² - 4x = 0
We can complete the square by adding and subtracting the same number to the equation. Now add and subtract 4 to it:
x² - 4x +4 - 4 = 0
⇒ x² - 4x +(2)² - 4 = 0
⇒ (x - 2)² -4 = 0
We have rewritten the equation by completing the square.
Therefore, we have rewritten the equation by completing the square as (x - 2)² -4 = 0.
Learn more about completing the square here: https://brainly.com/question/1596209
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