Answer:
x = [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
Given
4x² = 4x - 1 ( Subtract 4x - 1 from both sides )
4x² - 4x + 1 = 0 ← in standard form
To factorise the quadratic
Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term
product = 4 × 1 = 4 and sum = - 4
The factors are - 2 and - 2
Use these factors to split the middle term
4x² - 2x - 2x + 1 = 0 ( factor the first/second and third/fourth terms )
2x(2x - 1) - 1(2x - 1) = 0 ← factor out (2x - 1) from each term
(2x - 1)(2x - 1) = 0
(2x - 1)² = 0
2x - 1 = 0 ⇒ 2x = 1 ⇒ x = [tex]\frac{1}{2}[/tex] with multiplicity 2
