How do you solve #x^2-x=6#?

1 Answer

Answer:

Set the trinomial equal to zero and factor into two binomials .

#x= 3 and x = -2#

Explanation:

# x^2 -x -6 = 6-6# This gives

# x^2 -x -6 = 0 #

The C value is negative this means one of the binomials must be negative and the other positive.
The B value is negative this means that the negative value is larger than the positive value.
The coefficient of the B is 1 This means that the two factors have a difference of 1

Factors of 6 are # 6xx1 and 2xx3#

2 and 3 have a difference of 1 so these are the factors that work
The 3 must be negative because it is larger and the 2 positive so

# ( x - 3)xx (x +2) = 0 #

Set each factor equal to zero and solve for each of the binomials to find the possible values for x.

# x - 3 = 0 # add 3 to both sides

# x -3 +3 = 0 +3 #

#x = 3 #

# x +2 = 0# subtract 2 from both sides

# x +2 -2 = 0 -2 # this gives

#x = -2 #