Answer:
x ≈ 9.69, 0.31
Step-by-step explanation:
Given:
(x - 2)² - 6x = 1
We'll expand the squared binomial on the left:
x² - 4x + 4 - 6x = 1
Group like terms:
x² - 10x + 4 = 1
Complete the square by adding 21 to both sides:
x² - 10x + 25 = 22
(x - 5)² = 22
And solve for x:
x - 5 = √22
x = 5 ± √22
x ≈ 9.69, 0.31
