How do you solve #x^2-5x=14#?

1 Answer

Answer:

Set up two binomials.
The sum of the two numbers must be -5 and the product -14.
Then solve for x

Explanation:

# x^2 -5x = 14#

Subtract 14 from both sides of the equation to equal 0

# x^2 -5x -14 = 14 -14 " "# (14-14 = 0) giving

# x^2 - 5x -14 = 0 #
The -14 indicates that one number must be positive and one number must be negative.

The -5 indicates that the negative number must be larger than the positive number.

Factor -14 The possibilities are # -2 xx +7, +2 xx -7, -1 xx +14, +1 xx -14#
The combination that works is # +2 xx -7,# so the binomials are

# ( x + 2) xx ( x-7) =0#

Now set both binomials equal to zero and solve for x

# x + 2 = 0 " "# Subtract 2 from both sides

# x +2 -2 = 0 -2" " (2-2 =0)# so

#x = -2#

# x -7 = 0" " # add 7 to both sides

# x -7 + 7 = 0 +7" " ( -7 +7 = 0)# so

#x = +7 #