It is probably easiest to divide by the coefficient of x^2 first. It may also be helpful to put the constant term on the right side of the equal sign.
2x^2 + 11x - 6 = 0
x^2 + (11/2)x - 3 = 0
x^2 + (11/2)x = 3
Now, we complete the square by adding the square of half the x coefficient.
X^2 + (11/2)x + (11/4)^2 = 3 + (11/4)^2 (x + 11/4)^2 = 3 + 7 9/16
(x + 11/4)^2 = 10 9/16 = 169/16 = (13/4)^2
Consult your text or teacher to see what final form the answer should have.
Taking the square root, we have
x + 11/4 = ±13/4
x = (-11 ± 13)/4
x = 1/2, or x = -6
Thus, the equation can be factored as
(x - 1/2)(x + 6) = 0
We can "rationalize" this by multiplying both sides by 2.
(2x - 1)(x + 6) = 0
2x^2 + 11x - 6 = 0
x^2 + (11/2)x - 3 = 0
x^2 + (11/2)x = 3
Now, we complete the square by adding the square of half the x coefficient.
X^2 + (11/2)x + (11/4)^2 = 3 + (11/4)^2 (x + 11/4)^2 = 3 + 7 9/16
(x + 11/4)^2 = 10 9/16 = 169/16 = (13/4)^2
Consult your text or teacher to see what final form the answer should have.
Taking the square root, we have
x + 11/4 = ±13/4
x = (-11 ± 13)/4
x = 1/2, or x = -6
Thus, the equation can be factored as
(x - 1/2)(x + 6) = 0
We can "rationalize" this by multiplying both sides by 2.
(2x - 1)(x + 6) = 0
