Solve by factoring:x^2 – 5x = 6?

Hi!!

Let's do it:

x² - 5x = 6;
x² - 5x + 6 = 0;

Now we must factorise that expression, x² - 5x - 6. To factor it we should try to divide it using Ruffini's method with the divisors of the independent term, 6.

6 = 2 ∙ 3.

The divisors are 1, -1, 2, -2, 3, -3, 6 and -6.

Let's divide it by x - 1.

(x² - 5x - 6)/(x - 1)

It isn't a exact division. 1 isn't a root.

Let's divide it by x + 1.

(x² - 5x - 6)/(x + 1) = (x - 6)

It IS a exact division. -1 and 6 are roots.

Therefore the factored form is:

x² - 5x - 6 = (x - 6)(x + 1)

We can now reinsert it into the equation:

(x - 6)(x + 1) = 0;
x - 6 = 0, x = 6
x + 1 = 0; x = -1

∴ x = 6 and x = -1

Well, bye hope it helped, Happy Xmas :D!!

x² - 5x = 6
x² - 5/2x = 6 + (- 5/2)²
x² - 5/2x = 24/4 + 25/4
(x - 5/2)² = 49/4
x - 5/2 = 7/2

= x - 5/2 - 7/2, = x - 12/2, = x - 6
= x - 5/2 + 7/2, = x + 2/2, = x + 1

x - 6 = 0, x = 6
x + 1 = 0, x = - 1

Answer: x = 6, - 1; (x - 6)(x + 1) are the factors.

Proof (x = 6):
6² - 5(6) = 6
36 - 30 = 6
6 = 6

Proof (x = - 1):
- 1² - 5(- 1) = 6
1 + 5 = 6
6 = 6

Proof (F.O.I.L.):
(x - 6)(x + 1) = 0
x² + x - 6x - 6 = 0
x² - 5x - 6 = 0
x² - 5x = 6

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Question Number 1 :
For this equation x^2 - 5*x = 6 , answer the following questions :
A. Use factorization to find the root of the equation !

Answer Number 1 :
First, we have to turn equation : x^2 - 5*x = 6 , into a*x^2+b*x+c=0 form.
x^2 - 5*x = 6 , move everything in the right hand side, to the left hand side of the equation
<=> x^2 - 5*x - ( 6 ) = 0 , which is the same with
<=> x^2 - 5*x + ( - 6 ) =0 , now open the bracket and we get
<=> x^2 - 5*x - 6 = 0

The equation x^2 - 5*x - 6 = 0 is already in a*x^2+b*x+c=0 form.
In that form, we can easily derive that the value of a = 1, b = -5, c = -6.

1A. Solve by Factorization

x^2 -5*x -6 = 0
Separate : ( x^2 +x ) + ( -6*x -6 ) = 0
Commutative Law : ( x^2 -6*x ) + ( x -6 ) = 0
Distributive Law : x*( x -6 ) + +*( x -6 ) = 0
Factor : ( x +1 )*( x -6 ) = 0

So the Polynomial have 2 roots :
x1 = -1
x2 = 6

x² - 5x - 6 = 0
(x - 6)(x + 1) = 0
x = 6 , x = - 1

x^2-5x=6
x^2-5x-6=0
(x-6)(x+1)=0
x=6 or -1

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

x + 1 = 0
x = -1

x - 6 = 0
x = 6

∴ x = -1 , 6

Subtract 6 so you get x^2 - 5x -6 = 0, then factor that equation.

(x+1)(x-6)

x^2 - 5x = 6

Your first step is to bring everything to the left hand side.

x^2 - 5x - 6 = 0

Next, factor this as normal. As a reminder, you want to look for two factors of the third term (-6) that add up to the middle term (-5).

(x + ?)(x + ?) = 0

These two numbers are: -6 and +1. Those go in the question marks.

(x - 6)(x + 1) = 0

Equate each term to 0 to solve for possible values of x.

x - 6 = 0
x = 6

x + 1 = 0
x = -1

Therefore,
x = {6, -1}

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