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Simplifying (-5p + -1)(-5p + -1) = (-85 + -17) + -72 Reorder the terms: (-1 + -5p)(-5p + -1) = (-85 + -17) + -72 Reorder the terms: (-1 + -5p)(-1 + -5p) = (-85 + -17) + -72 Multiply (-1 + -5p) * (-1 + -5p) (-1(-1 + -5p) + -5p * (-1 + -5p)) = (-85 + -17) + -72 ((-1 * -1 + -5p * -1) + -5p * (-1 + -5p)) = (-85 + -17) + -72 ((1 + 5p) + -5p * (-1 + -5p)) = (-85 + -17) + -72 (1 + 5p + (-1 * -5p + -5p * -5p)) = (-85 + -17) + -72 (1 + 5p + (5p + 25p2)) = (-85 + -17) + -72 Combine like terms: 5p + 5p = 10p (1 + 10p + 25p2) = (-85 + -17) + -72 Combine like terms: -85 + -17 = -102 1 + 10p + 25p2 = (-102) + -72 1 + 10p + 25p2 = -102 + -72 Combine like terms: -102 + -72 = -174 1 + 10p + 25p2 = -174 Solving 1 + 10p + 25p2 = -174 Solving for variable 'p'. Reorder the terms: 1 + 174 + 10p + 25p2 = -174 + 174 Combine like terms: 1 + 174 = 175 175 + 10p + 25p2 = -174 + 174 Combine like terms: -174 + 174 = 0 175 + 10p + 25p2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(35 + 2p + 5p2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(35 + 2p + 5p2)' equal to zero and attempt to solve: Simplifying 35 + 2p + 5p2 = 0 Solving 35 + 2p + 5p2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 7 + 0.4p + p2 = 0 Move the constant term to the right: Add '-7' to each side of the equation. 7 + 0.4p + -7 + p2 = 0 + -7 Reorder the terms: 7 + -7 + 0.4p + p2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 0.4p + p2 = 0 + -7 0.4p + p2 = 0 + -7 Combine like terms: 0 + -7 = -7 0.4p + p2 = -7 The p term is 0.4p. Take half its coefficient (0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. 0.4p + 0.04 + p2 = -7 + 0.04 Reorder the terms: 0.04 + 0.4p + p2 = -7 + 0.04 Combine like terms: -7 + 0.04 = -6.96 0.04 + 0.4p + p2 = -6.96 Factor a perfect square on the left side: (p + 0.2)(p + 0.2) = -6.96 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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