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Answer:
[tex]x^2+12x-220=0[/tex] -- Proved
[tex]x = 10\ \ \ x = -22[/tex]
Step-by-step explanation:
Given
[tex]Volume = 924cm^3[/tex]
[tex]Dimension: 4cm; (x+1)cm; (x+11)cm[/tex]
Required
Show that [tex]x^2+12x-220=0[/tex]
The volume is calculated as:
[tex]4 * (x + 1) * (x + 11) = 924[/tex]
Open the brackets
[tex](4x + 4) * (x + 11) = 924[/tex]
[tex]4x^2 + 44x + 4x + 44 = 924[/tex]
[tex]4x^2 + 48x+ 44 = 924[/tex]
Collect Like Terms
[tex]4x^2 + 48x+ 44 - 924=0[/tex]
[tex]4x^2 + 48x -880=0[/tex]
Divide through by 4
[tex]\frac{4x^2}{4} + \frac{48x}{4} -\frac{880}{4}=0[/tex]
[tex]x^2+12x-220=0[/tex]
Solving further:
Expand the expression
[tex]x^2 + 22x - 10x - 220 = 0[/tex]
Factorize:
[tex]x(x + 22) - 10(x + 22) = 0[/tex]
[tex](x - 10)(x + 22) = 0[/tex]
Split:
[tex]x - 10 = 0;\ \ \ x + 22 = 0[/tex]
[tex]x = 10\ \ \ x = -22[/tex]