Answer:
see explanation
Step-by-step explanation:
(a)
x² - 6x + 4 = 0 ( subtract 4 from both sides )
x² - 6x = - 4
To complete the square
add ( half the coefficient of the x- term )² to both sides
x² + 2(- 3)x + 9 = - 4 + 9
(x - 3)² = 5 ( take the square root of both sides )
x - 3 = ± [tex]\sqrt{5}[/tex] ( add 3 to both sides )
x = 3 ± [tex]\sqrt{5}[/tex] ← exact solutions
(b)
4x² + 16x + 9 = 0
To complete the square
The coefficient of the x² term must be 1
Factor out 4 from 4x² + 16x
4(x² + 4x) + 9 = 0
add/subtract ( half the coefficient of the x- term )² to x² + 4x
4(x² + 2(2)x + 4 - 4 ) + 9 = 0
4(x + 2)² - 16 + 9 = 0
4(x + 2)² - 7 = 0 ( add 7 to both sides )
4(x + 2)² = 7 ( divide both sides by 4 )
(x + 2)² = [tex]\frac{7}{4}[/tex] ( take the square root of both sides )
x + 2 = ± [tex]\sqrt{\frac{7}{4} }[/tex] = ± [tex]\frac{\sqrt{7} }{2}[/tex] ( subtract 2 from both sides )
x = - 2 ± [tex]\frac{\sqrt{7} }{2}[/tex] ← exact solutions
