Question

factorizr.

1) x^2=5x-6
2) 6x^2-20=-7x
3) 6x^2-7x=-2

Answer 1

1. x^2 = 5x-6,
x^2 - 5x + 6 = 0,
(x-2)(x-3) = 0.

x-2 = 0.
x = 2.

(x-3) = 0,
x = 3.

Solution Set: x = 2, and 3.

2. 6x^2 - 20 = - 7x,
6x^2 + 7x -20 = 0,
Use AC Method:
A*C = 6*(-20) = -120 = -4*30 = -5*24 =
-6*20 = -8*15.
Select the factored pair whose sum =
the coefficient of x(7):
6x^2 - 8x+15x - 20 = 0,
Group the 4 terms into 2 factorable pairs:
(6x^2-8x) + (15x-20) = 0,
2x(3x-4) + 5(3x-4) = 0,
(3x-4)(2x+5) = 0,

3x-4 = 0,
3x = 4,
x = 4/3 = 1 1/3.

2x+5 = 0,
2x = -5.
x = -5/2 = -2 1/2.

Solution Set: x = 1 1/3, and -2 1/2.

3. Use same procedure as problem 2 and get:
x = 2/3, and 1/2.