Completing the square?

Question

2x2-2x-4=0
3x2-9x-12=0
2x2-6x-5=0

Answer 1

Q1) 2x^2 - 2x - 4 = 0

Divide out the coefficient of x^2

x^2 - x - 2 = 0

Move the constant to the other side

x^2 - x = 2

Half and square the coefficient of x and add to both sides

x^2 - x + 1/4 = 2 + 1/4

Write the left as a binomial square and simplify the right

(x - 1/2)^2 = 9/4

Take the square root

x - 1/2 = +/- 3/2

Add 1/2 and simplify

x = 1/2 +/-3/2

x = 1/2 + 3/2 = 2
x = 1/2 - 3/2 = -1

The solutions are x = -1 and 2

Q2)

3x^2 - 9x - 12 = 0

x^2 - 3x - 4 = 0

x^2 - 3x = 4

x^2 - 3x + 9/4 = 4 + 9/4

(x - 3/2)^2 = 25/4

x - 3/2 = +/- 5/2

x = 3/2 +- 5/2

x = -1 and 4

Q3) 2x^2 - 6x - 5 = 0

x^2 - 3x - 5/2 = 0

x^2 - 3x = 5/2

x^2 - 3x + 9/4 = 5/2 + 9/4

(x - 3/2)^2 = 19/4

x - 3/2 = +/- SQRT (19) / 2

x = 3/2 +/- SQRT (19) / 2

Answer 2

Question 1
x² - x - 2 = 0
(x - 2).(x + 1) = 0
x = 2, x = -1

Question 2
x² - 3x - 4 = 0
(x - 4).(x + 1) = 0
x = 4, x = - 1

Question 3
x² - 3x - 5/2 = 0
(x² - 3x + 9/4) - 9/4 - 10/4 = 0
(x - 3 / 2)² = 19/4
(x - 3 / 2) = ±√19 / 2
x = 3 / 2 ± √19 / 2
x = - 3 / 2 ±√19 / 2
x = (1/2).(- 3 ± √19)