factorizr.
1) x^2=5x-6
2) 6x^2-20=-7x
3) 6x^2-7x=-2
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.
To factorize the given equations, we need to rewrite them in quadratic form (ax^2 + bx + c = 0) and then find the factors. Let's go through each equation step by step:
1) x^2 = 5x - 6
To factorize this equation, we need to rearrange it in quadratic form. Move all terms to one side of the equation:
x^2 - 5x + 6 = 0
Now, we need to find two numbers that multiply to give us 6 and add up to give us -5 (the coefficient of x). The numbers -2 and -3 satisfy these conditions, so we can write:
(x - 2)(x - 3) = 0
Therefore, the factors of the equation are (x - 2) and (x - 3).
2) 6x^2 - 20 = -7x
Rearranging the equation gives us:
6x^2 + 7x - 20 = 0
To factorize this equation, we need to find two numbers that multiply to give us -120 (6 * -20) and add up to give us 7 (the coefficient of x). The numbers 15 and -8 satisfy these conditions, so we can write:
(2x + 5)(3x - 4) = 0
Thus, the factors of the equation are (2x + 5) and (3x - 4).
3) 6x^2 - 7x = -2
We can rewrite the equation in quadratic form by moving all terms to one side:
6x^2 - 7x + 2 = 0
To factorize this equation, we look for two numbers that multiply to give us 12 (6 * 2) and add up to give us -7 (the coefficient of x). The numbers -3 and -4 satisfy these conditions, so we can write:
(2x - 1)(3x - 2) = 0
So, the factors of the equation are (2x - 1) and (3x - 2).
These are the factorized forms of the given equations.