Answer:
x = 4 ± [tex]\sqrt{30}[/tex]
Step-by-step explanation:
Given
x² - 8x - 14 = 0 ( add 14 to both sides )
x² - 8x = 14
To complete the square
add ( half the coefficient of the x- term )² to both sides
x² + 2(- 4)x + 16 = 14 + 16, that is
(x - 4)² = 30 ( take the square root of both sides )
x - 4 = ± [tex]\sqrt{30}[/tex] ( add 4 to both sides )
x = 4 ± [tex]\sqrt{30}[/tex], thus the exact solutions are
x = 4 - [tex]\sqrt{30}[/tex]
x = 4 + [tex]\sqrt{30}[/tex]
