Respuesta :
Answer:
x = - [tex]\frac{1}{2}[/tex], x = [tex]\frac{3}{2}[/tex]
Step-by-step explanation:
Given
x² - x - [tex]\frac{3}{4}[/tex] = 0 ( add [tex]\frac{3}{4}[/tex] to both sides )
x² - x = [tex]\frac{3}{4}[/tex]
Solve using the method of completing the square
add ( half the coefficient of the x- term )² to both sides
x² + 2( - [tex]\frac{1}{2}[/tex] )x + [tex]\frac{1}{4}[/tex] = [tex]\frac{3}{4}[/tex] + [tex]\frac{1}{4}[/tex]
(x - [tex]\frac{1}{2}[/tex] )² = 1 ( take the square root of both sides )
x - [tex]\frac{1}{2}[/tex] = ± 1 ( add [tex]\frac{1}{2}[/tex] to both sides )
x = [tex]\frac{1}{2}[/tex] ± 1
Thus
x = [tex]\frac{1}{2}[/tex] - 1 = - [tex]\frac{1}{2}[/tex]
x = [tex]\frac{1}{2}[/tex] + 1 = [tex]\frac{3}{2}[/tex]
