How do you solve x^2-5x=14x2−5x=14?

1 Answer
David Drayer · EZ as pi
Mar 22, 2017

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 = 14x2−5x=14

Subtract 14 from both sides of the equation to equal 0

x^2 -5x -14 = 14 -14 " "x2−5x−14=14−14 (14-14 = 0) giving

x^2 - 5x -14 = 0 x2−5x−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 -14−2×+7,+2×−7,−1×+14,+1×−14
The combination that works is +2 xx -7,+2×−7, so the binomials are

( x + 2) xx ( x-7) =0(x+2)×(x−7)=0

Now set both binomials equal to zero and solve for x

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

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

x = -2x=−2

x -7 = 0" " x−7=0 add 7 to both sides

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

x = +7 x=+7

Related questions
See all questions in Zero Product Principle
Impact of this question
17710 views around the world
You can reuse this answer
Creative Commons License