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Solve for x V=(x)(22-2x)(22-2x)

Problem

V=x*(22−2*x)*(22−2*x)

Solution

  1. Identify the equation as a cubic equation where V is a function of x and we need to solve for x in terms of V

  2. Simplify the expression by factoring out a 2 from each binomial term.

V=x*[2*(11−x)]*[2*(11−x)]

  1. Combine the constant factors.

V=4*x*(11−x)2

  1. Expand the squared binomial (11−x)2

V=4*x*(121−22*x+x2)

  1. Distribute the 4*x into the parentheses to write the equation in standard cubic form.

V=4*x3−88*x2+484*x

  1. Rearrange the equation into the form a*x3+b*x2+c*x+d=0

4*x3−88*x2+484*x−V=0

  1. Divide the entire equation by 4 to simplify the coefficients.

x3−22*x2+121*x−V/4=0

  1. Recognize that solving a general cubic equation for x involves the cubic formula, which results in complex expressions. For specific values of V numerical methods or the cubic formula can be applied to find the roots.

Final Answer

x3−22*x2+121*x−V/4=0

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