Equations! please help

Question

consider the equation x²-6x-40=0. Make sure to show your work for each part.

a) Solve the equation by factoring and using the zero product rule

b)solve the equation by completing the square and and applying square root pinciple.

c)Sole equation using quadric formula

Answer 1

a) x² - 6x - 40 = 0

-> (x - 10)•(x + 4) = 0

By the zero product rule,

x - 10 = 0 and/or x + 4 = 0

-> x = 10, x = -4

b) x² - 6x = 40 (Add 40 to both sides to bring the 40 on the right side of the equal sign)

-> x² - 6x + (-6/2)² = 40 + (-6/2)² (Add (b/2)² to both sides where b = -6)

-> x² - 6x + 9 = 40 + 9 (Simplify)

-> (x - 3)² = 49 (We get a perfect square on the LHS and obtain a squared binomial)

-> √(x - 3)² = √49 (Square root both sides)

-> x - 3 = ±7

-> x - 3 = 7 or x - 3 = -7

-> x = 10 or x = -4

c) x = (-b ± √b² - 4ac) / 2a

-> x = [-(-6) ± √(-6)² - 4(1)(-40)] / 2(1)

-> x = (6 ± √36 + 160 ) / 2

-> x = (6 ± √196) / 2

-> x = (6 ± 14) / 2

-> x = (6 + 14) / 2 OR x = (6 - 14) / 2

-> x = 10 or x = -4