SOLUTION: 4x(x-9)-5x(x-8)=-5

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Question 283328: 4x(x-9)-5x(x-8)=-5
Found 2 solutions by mananth, Deina:
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
4x(x-9)-5x(x-8)=-5
4x^2-36x-5x^2+40x=-5
-x^2+4x+5=0
x^2-4x-5=0
x^2-5x+x-5=0
x(x-5)+1(x-5)=0
(x+1)(x-5)=0

Answer by Deina(147) About Me  (Show Source):
You can put this solution on YOUR website!
First we need to simplify the equation:
4*x*(x-9)-5*x*(x-8)=-5
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • This is an equation! Solutions: x=-1,x=5.
  • Graphical form: Equation 4%2Ax%2A%28x-9%29-5%2Ax%2A%28x-8%29=-5 was fully solved.
  • Text form: 4*x*(x-9)-5*x*(x-8)=-5 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+4%2Ax%2A%28x-9%29-5%2Ax%2A%28x-8%29=-5+%29
    For tutors: simplify_cartoon( 4*x*(x-9)-5*x*(x-8)=-5 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at 4%2Ax%2A%28x-9%29-5%2Ax%2A%28x-8%29=highlight_red%28+-5+%29.
Moved these terms to the left highlight_green%28+5+%29
It becomes 4%2Ax%2A%28x-9%29-5%2Ax%2A%28x-8%29%2Bhighlight_green%28+5+%29=0.
Look at highlight_red%28+4%2Ax%2A%28x-9%29+%29-5%2Ax%2A%28x-8%29%2B5=0.
Expanded term 4%2Ax by using associative property on %28x-9%29
It becomes highlight_green%28+4%2Ax%2Ax+%29-highlight_green%28+4%2Ax%2A9+%29-5%2Ax%2A%28x-8%29%2B5=0.
Look at 4%2Ax%2Ax-highlight_red%28+4+%29%2Ax%2Ahighlight_red%28+9+%29-5%2Ax%2A%28x-8%29%2B5=0.
Multiplied numerator integers
It becomes 4%2Ax%2Ax-highlight_green%28+36+%29%2Ax-5%2Ax%2A%28x-8%29%2B5=0.
Look at 4%2Ahighlight_red%28+x+%29%2Ahighlight_red%28+x+%29-36%2Ax-5%2Ax%2A%28x-8%29%2B5=0.
Reduce similar several occurrences of highlight_red%28+x+%29 to highlight_green%28+x%5E2+%29
It becomes 4%2Ahighlight_green%28+x%5E2+%29-36%2Ax-5%2Ax%2A%28x-8%29%2B5=0.
Look at 4%2Ax%5E2-36%2Ax-highlight_red%28+5%2Ax%2A%28x-8%29+%29%2B5=0.
Expanded term -5%2Ax by using associative property on %28x-8%29
It becomes 4%2Ax%5E2-36%2Ax-highlight_green%28+5%2Ax%2Ax+%29%2Bhighlight_green%28+5%2Ax%2A8+%29%2B5=0.
Look at 4%2Ax%5E2-36%2Ax-5%2Ax%2Ax%2Bhighlight_red%28+5+%29%2Ax%2Ahighlight_red%28+8+%29%2B5=0.
Multiplied numerator integers
It becomes 4%2Ax%5E2-36%2Ax-5%2Ax%2Ax%2Bhighlight_green%28+40+%29%2Ax%2B5=0.
Look at 4%2Ax%5E2-36%2Ax-5%2Ahighlight_red%28+x+%29%2Ahighlight_red%28+x+%29%2B40%2Ax%2B5=0.
Reduce similar several occurrences of highlight_red%28+x+%29 to highlight_green%28+x%5E2+%29
It becomes 4%2Ax%5E2-36%2Ax-5%2Ahighlight_green%28+x%5E2+%29%2B40%2Ax%2B5=0.
Look at highlight_red%28+4%2Ax%5E2+%29-36%2Ax-highlight_red%28+5%2Ax%5E2+%29%2B40%2Ax%2B5=0.
Eliminated similar terms highlight_red%28+4%2Ax%5E2+%29,highlight_red%28+-5%2Ax%5E2+%29 replacing them with highlight_green%28+%284-5%29%2Ax%5E2+%29
It becomes highlight_green%28+%284-5%29%2Ax%5E2+%29-36%2Ax%2B40%2Ax%2B5=0.
Look at %284-5%29%2Ax%5E2-highlight_red%28+36%2Ax+%29%2Bhighlight_red%28+40%2Ax+%29%2B5=0.
Eliminated similar terms highlight_red%28+-36%2Ax+%29,highlight_red%28+40%2Ax+%29 replacing them with highlight_green%28+%28-36%2B40%29%2Ax+%29
It becomes %284-5%29%2Ax%5E2%2Bhighlight_green%28+%28-36%2B40%29%2Ax+%29%2B5=0.
Look at %28highlight_red%28+4+%29-highlight_red%28+5+%29%29%2Ax%5E2%2B%28-36%2B40%29%2Ax%2B5=0.
Added fractions or integers together
It becomes %28highlight_green%28+-1+%29%29%2Ax%5E2%2B%28-36%2B40%29%2Ax%2B5=0.
Look at %28-1%29%2Ax%5E2%2B%28-highlight_red%28+36+%29%2Bhighlight_red%28+40+%29%29%2Ax%2B5=0.
Added fractions or integers together
It becomes %28-1%29%2Ax%5E2%2B%28highlight_green%28+4+%29%29%2Ax%2B5=0.
Look at %28highlight_red%28+-1+%29%29%2Ax%5E2%2B%284%29%2Ax%2B5=0.
Removed extra sign in front of -1
It becomes %28-highlight_green%28+1+%29%29%2Ax%5E2%2B%284%29%2Ax%2B5=0.
Look at highlight_red%28+%28-highlight_red%28+1+%29%29%2Ax%5E2+%29%2B%284%29%2Ax%2B5=0.
Remove unneeded parentheses around factor highlight_red%28+1+%29
It becomes -highlight_green%28+1+%29%2Ax%5E2%2B%284%29%2Ax%2B5=0.
Look at -1%2Ax%5E2%2Bhighlight_red%28+%28highlight_red%28+4+%29%29%2Ax+%29%2B5=0.
Remove unneeded parentheses around factor highlight_red%28+4+%29
It becomes -1%2Ax%5E2%2Bhighlight_green%28+4+%29%2Ax%2B5=0.
Look at -highlight_red%28+1+%29%2Ax%5E2%2B4%2Ax%2B5=0.
Remove extraneous '1' from product highlight_red%28+1+%29
It becomes -x%5E2%2B4%2Ax%2B5=0.
Look at highlight_red%28+-x%5E2%2B4%2Ax%2B5+%29=0.
Equation highlight_red%28+-x%5E2%2B4%2Ax%2B5=0+%29 is a quadratic equation: -x^2+4*x+5 =0, and has solutions -1,5
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=-1,x=5.

Universal Simplifier and Solver


Done!


Notice that this turns it into the quadratic -x%5E2+%2B+4%2Ax+%2B+5+=+0, which you can solve as any standard quadratic in the form of x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ and bob's your uncle!