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Simplifying -4p2 + 20p + -400 = 0 Reorder the terms: -400 + 20p + -4p2 = 0 Solving -400 + 20p + -4p2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '4'. 4(-100 + 5p + -1p2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-100 + 5p + -1p2)' equal to zero and attempt to solve: Simplifying -100 + 5p + -1p2 = 0 Solving -100 + 5p + -1p2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 100 + -5p + p2 = 0 Move the constant term to the right: Add '-100' to each side of the equation. 100 + -5p + -100 + p2 = 0 + -100 Reorder the terms: 100 + -100 + -5p + p2 = 0 + -100 Combine like terms: 100 + -100 = 0 0 + -5p + p2 = 0 + -100 -5p + p2 = 0 + -100 Combine like terms: 0 + -100 = -100 -5p + p2 = -100 The p term is -5p. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5p + 6.25 + p2 = -100 + 6.25 Reorder the terms: 6.25 + -5p + p2 = -100 + 6.25 Combine like terms: -100 + 6.25 = -93.75 6.25 + -5p + p2 = -93.75 Factor a perfect square on the left side: (p + -2.5)(p + -2.5) = -93.75 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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