SOLUTION: {{{6(6x+9)=x(5x)}}}

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Question 306539: 6%286x%2B9%29=x%285x%29
Found 2 solutions by checkley77, ichudov:
Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
6(6x+9)=x(5x)
36x+54=5x^2
5x^2-36x-54=0
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x=(36+-sqrt[-36^2-4*5*-54])/2*5
x=(36+-sqrt[1,296+1.080])/10
x=(36+-sqrt2,376)/10
x=(36+-48.74)/10
x=(36+48.74)/10
x=84.74/10
x=8.474 ans.
x=(36-48.74)/10
x=-12.74/10
x=-1.274 ans.

Answer by ichudov(507) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • This is an equation! Solutions: x=-1.27442304278158,x=8.47442304278158.
  • Graphical form: Equation 6%2A%286x%2B9%29=x%2A%285x%29 was fully solved.
  • Text form: 6*(6x+9)=x*(5x) simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+6%2A%286x%2B9%29=x%2A%285x%29+%29
    For tutors: simplify_cartoon( 6*(6x+9)=x*(5x) )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at 6%2A%286%2Ax%2B9%29=highlight_red%28+x%2A%28highlight_red%28+5%2Ax+%29%29+%29.
Remove unneeded parentheses around factor highlight_red%28+5+%29,highlight_red%28+x+%29
It becomes 6%2A%286%2Ax%2B9%29=x%2Ahighlight_green%28+5+%29%2Ahighlight_green%28+x+%29.
Look at 6%2A%286%2Ax%2B9%29=highlight_red%28+x+%29%2A5%2Ahighlight_red%28+x+%29.
Reduce similar several occurrences of highlight_red%28+x+%29 to highlight_green%28+x%5E2+%29
It becomes 6%2A%286%2Ax%2B9%29=highlight_green%28+x%5E2+%29%2A5.
Look at 6%2A%286%2Ax%2B9%29=highlight_red%28+x%5E2%2A5+%29.
Moved these terms to the left highlight_green%28+-x%5E2%2A5+%29
It becomes 6%2A%286%2Ax%2B9%29-highlight_green%28+x%5E2%2A5+%29=0.
Look at highlight_red%28+6%2A%286%2Ax%2B9%29+%29-x%5E2%2A5=0.
Expanded term 6 by using associative property on %286%2Ax%2B9%29
It becomes highlight_green%28+6%2A6%2Ax+%29%2Bhighlight_green%28+6%2A9+%29-x%5E2%2A5=0.
Look at highlight_red%28+6+%29%2Ahighlight_red%28+6+%29%2Ax%2B6%2A9-x%5E2%2A5=0.
Multiplied numerator integers
It becomes highlight_green%28+36+%29%2Ax%2B6%2A9-x%5E2%2A5=0.
Look at 36%2Ax%2Bhighlight_red%28+6+%29%2Ahighlight_red%28+9+%29-x%5E2%2A5=0.
Multiplied numerator integers
It becomes 36%2Ax%2Bhighlight_green%28+54+%29-x%5E2%2A5=0.
Look at 36%2Ax%2Bhighlight_red%28+54+%29-x%5E2%2A5=0.
Moved 54 to the right of expression
It becomes 36%2Ax-x%5E2%2A5%2Bhighlight_green%28+54+%29=0.
Look at highlight_red%28+36%2Ax-x%5E2%2A5%2B54+%29=0.
Equation highlight_red%28+36%2Ax-x%5E2%2A5%2B54=0+%29 is a quadratic equation: -5*x^2+36*x+54 =0, and has solutions -1.27442304278158,8.47442304278158
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=-1.27442304278158,x=8.47442304278158.

Universal Simplifier and Solver


Done!