SOLUTION: a rectangular box has volume 280^3in. its dimensions are 4in. x(n+2)in. x(n+5)in. find n. use the formula v=lwh

Algebra ->  Equations -> SOLUTION: a rectangular box has volume 280^3in. its dimensions are 4in. x(n+2)in. x(n+5)in. find n. use the formula v=lwh      Log On


   

Question 306892: a rectangular box has volume 280^3in. its dimensions are 4in. x(n+2)in. x(n+5)in. find n. use the formula v=lwh
Answer by ichudov(507) About Me  (Show Source):
You can put this solution on YOUR website!
4*(n+2)*(n+5)=280
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • This is an equation! Solutions: n=5,n=-12.
  • Graphical form: Equation 4%2A%28n%2B2%29%2A%28n%2B5%29=280 was fully solved.
  • Text form: 4*(n+2)*(n+5)=280 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+4%2A%28n%2B2%29%2A%28n%2B5%29=280+%29
    For tutors: simplify_cartoon( 4*(n+2)*(n+5)=280 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at 4%2A%28n%2B2%29%2A%28n%2B5%29=highlight_red%28+280+%29.
Moved these terms to the left highlight_green%28+-280+%29
It becomes 4%2A%28n%2B2%29%2A%28n%2B5%29-highlight_green%28+280+%29=0.
Look at highlight_red%28+4%2A%28n%2B2%29%2A%28n%2B5%29+%29-280=0.
Expanded term 4%2A%28n%2B5%29 by using associative property on %28n%2B2%29
It becomes .
Look at 4%2A%28n%2B5%29%2An%2Bhighlight_red%28+4+%29%2A%28n%2B5%29%2Ahighlight_red%28+2+%29-280=0.
Multiplied numerator integers
It becomes 4%2A%28n%2B5%29%2An%2Bhighlight_green%28+8+%29%2A%28n%2B5%29-280=0.
Look at highlight_red%28+4%2A%28n%2B5%29%2An+%29%2B8%2A%28n%2B5%29-280=0.
Expanded term 4%2An by using associative property on %28n%2B5%29
It becomes highlight_green%28+4%2An%2An+%29%2Bhighlight_green%28+4%2An%2A5+%29%2B8%2A%28n%2B5%29-280=0.
Look at 4%2An%2An%2Bhighlight_red%28+4+%29%2An%2Ahighlight_red%28+5+%29%2B8%2A%28n%2B5%29-280=0.
Multiplied numerator integers
It becomes 4%2An%2An%2Bhighlight_green%28+20+%29%2An%2B8%2A%28n%2B5%29-280=0.
Look at 4%2Ahighlight_red%28+n+%29%2Ahighlight_red%28+n+%29%2B20%2An%2B8%2A%28n%2B5%29-280=0.
Reduce similar several occurrences of highlight_red%28+n+%29 to highlight_green%28+n%5E2+%29
It becomes 4%2Ahighlight_green%28+n%5E2+%29%2B20%2An%2B8%2A%28n%2B5%29-280=0.
Look at 4%2An%5E2%2B20%2An%2Bhighlight_red%28+8%2A%28n%2B5%29+%29-280=0.
Expanded term 8 by using associative property on %28n%2B5%29
It becomes 4%2An%5E2%2B20%2An%2Bhighlight_green%28+8%2An+%29%2Bhighlight_green%28+8%2A5+%29-280=0.
Look at 4%2An%5E2%2B20%2An%2B8%2An%2Bhighlight_red%28+8+%29%2Ahighlight_red%28+5+%29-280=0.
Multiplied numerator integers
It becomes 4%2An%5E2%2B20%2An%2B8%2An%2Bhighlight_green%28+40+%29-280=0.
Look at 4%2An%5E2%2B20%2An%2B8%2An%2Bhighlight_red%28+40+%29-highlight_red%28+280+%29=0.
Added fractions or integers together
It becomes 4%2An%5E2%2B20%2An%2B8%2An%2Bhighlight_green%28+-240+%29=0.
Look at 4%2An%5E2%2B20%2An%2B8%2An%2Bhighlight_red%28+-240+%29=0.
Removed extra sign in front of -240
It becomes 4%2An%5E2%2B20%2An%2B8%2An-highlight_green%28+240+%29=0.
Look at 4%2An%5E2%2Bhighlight_red%28+20%2An+%29%2Bhighlight_red%28+8%2An+%29-240=0.
Eliminated similar terms highlight_red%28+20%2An+%29,highlight_red%28+8%2An+%29 replacing them with highlight_green%28+%2820%2B8%29%2An+%29
It becomes 4%2An%5E2%2Bhighlight_green%28+%2820%2B8%29%2An+%29-240=0.
Look at 4%2An%5E2%2B%28highlight_red%28+20+%29%2Bhighlight_red%28+8+%29%29%2An-240=0.
Added fractions or integers together
It becomes 4%2An%5E2%2B%28highlight_green%28+28+%29%29%2An-240=0.
Look at 4%2An%5E2%2Bhighlight_red%28+%28highlight_red%28+28+%29%29%2An+%29-240=0.
Remove unneeded parentheses around factor highlight_red%28+28+%29
It becomes 4%2An%5E2%2Bhighlight_green%28+28+%29%2An-240=0.
Look at highlight_red%28+4%2An%5E2%2B28%2An-240+%29=0.
Equation highlight_red%28+4%2An%5E2%2B28%2An-240=0+%29 is a quadratic equation: 4*n^2+28*n-240 =0, and has solutions 5,-12
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: n=5,n=-12.

Universal Simplifier and Solver


Done!


Solution n=-12 will not work since lengths can only be positive. So the answer is 5.