Solve 3x^2-9x=7 by completing the square.?

Answer 1

Well, divide over the 3:

x² - 3x = 7/3

To complete the square, you add (3/2)² to both sides - in general, it's (b/2)² you add to both sides:

x² - 3x + 9/4 = 7/3 + 9/4 = 55/12

Now simplify the square:

(x-3/2)² = 55/12

take the square root:

x - 3/2 = ± √(55/12)

x = 3/2 ± √(55/12)

You can simplify it, if you want:

x = 3/2 ± √(55/12)

x = 3/2 ± √(12×55)/12

x = 18/12 ± √(12×55)/12

x = [18 ± 2√(3×55) ] / 12

x = [9 ± √(3×55) ] / 6

x = [9 ± √(165) ] / 6

Answer 2

3x^2 - 9x = 7
x^2 - 3x = 7/3
x^2 - 3x + 9/4 = 7/3 + 9/4
x^2 - 3x + 9/4 = 27/12 + 28/12 = 55/12
(x - 3/2)^2 = 55/12
x - 3/2 = +-sqrt(55/12) = +-sqrt(165/36) = +-sqrt(165)/6
x = +-sqrt(165)/6 + 3/2 = +-sqrt(165)/6 + 9/6
x = [9 +-sqrt(165) ] / 6

Answer 3

3(x ² - 3 x) = 7
3(x ² - 9 x + 9 - 9) = 7
(x ² - 9 x + 9) - 27 = 7
(x - 3)² = 34
(x - 3) = ±√34
x = 3 ± √34