SOLUTION: solve for x: 4x(x-5)-5x(x-4)=-1

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Question 624779: solve for x: 4x(x-5)-5x(x-4)=-1
Answer by reynard2007(52) About Me  (Show Source):
You can put this solution on YOUR website!
Here's how I did it:
4x%28x-5%29++-++5x%28x-4%29+=+-1 This is given
4x%5E2-20x+-+5x%5E2%2B20x=-1 Distribute 4x and -5x to the contents of the parenthesis next to them. DPMA?
-x%5E2=-1 Add like terms: 4x%5E2%2B-5x%5E2 and -20x%2B20x
-x%5E2%2B1=0 Transpose -1 to the other side of the equation, which makes it positive
x%5E2-1=0 In solving equations like this, oyu are allowed to multiply a number to both sides of the equation, so long as you do it for both sides of the equation. Here, multiply -1 to both sides turning -x%5E2 to positive x%5E2 and %2B1 to -1
If you are familiar with the special product called DOTS (Difference of two squares) this will make solving the equation easier. Given x%5E2-1=0 you can factor it to %28x%2B1%29 and %28x-1%29. Equate both of these to 0 and you get:
x%2B1=0 -->x=-1
and
x-1=0 --> x=1


I can't find a way to reply to your comment so, I just edited this.
when x=1;
4%2A%281%29%2A%28%281%29-5%29++-++5%2A%281%29%2A%28%281%29-4%29+=+-1
4%2A%28-4%29-5%2A%28-3%29=-1
-16-%28-15%29=-16%2B15=-1
You can try the same with x=-1
Hope this does it for your problem.