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Simplifying 84300 = -8p + 0.6p2 Solving 84300 = -8p + 0.6p2 Solving for variable 'p'. Reorder the terms: 84300 + 8p + -0.6p2 = -8p + 8p + 0.6p2 + -0.6p2 Combine like terms: -8p + 8p = 0 84300 + 8p + -0.6p2 = 0 + 0.6p2 + -0.6p2 84300 + 8p + -0.6p2 = 0.6p2 + -0.6p2 Combine like terms: 0.6p2 + -0.6p2 = 0.0 84300 + 8p + -0.6p2 = 0.0 Begin completing the square. Divide all terms by -0.6 the coefficient of the squared term: Divide each side by '-0.6'. -140500 + -13.33333333p + p2 = 0 Move the constant term to the right: Add '140500' to each side of the equation. -140500 + -13.33333333p + 140500 + p2 = 0 + 140500 Reorder the terms: -140500 + 140500 + -13.33333333p + p2 = 0 + 140500 Combine like terms: -140500 + 140500 = 0 0 + -13.33333333p + p2 = 0 + 140500 -13.33333333p + p2 = 0 + 140500 Combine like terms: 0 + 140500 = 140500 -13.33333333p + p2 = 140500 The p term is -13.33333333p. Take half its coefficient (-6.666666665). Square it (44.44444442) and add it to both sides. Add '44.44444442' to each side of the equation. -13.33333333p + 44.44444442 + p2 = 140500 + 44.44444442 Reorder the terms: 44.44444442 + -13.33333333p + p2 = 140500 + 44.44444442 Combine like terms: 140500 + 44.44444442 = 140544.44444442 44.44444442 + -13.33333333p + p2 = 140544.44444442 Factor a perfect square on the left side: (p + -6.666666665)(p + -6.666666665) = 140544.44444442 Calculate the square root of the right side: 374.892577206 Break this problem into two subproblems by setting (p + -6.666666665) equal to 374.892577206 and -374.892577206.Subproblem 1
p + -6.666666665 = 374.892577206 Simplifying p + -6.666666665 = 374.892577206 Reorder the terms: -6.666666665 + p = 374.892577206 Solving -6.666666665 + p = 374.892577206 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '6.666666665' to each side of the equation. -6.666666665 + 6.666666665 + p = 374.892577206 + 6.666666665 Combine like terms: -6.666666665 + 6.666666665 = 0.000000000 0.000000000 + p = 374.892577206 + 6.666666665 p = 374.892577206 + 6.666666665 Combine like terms: 374.892577206 + 6.666666665 = 381.559243871 p = 381.559243871 Simplifying p = 381.559243871Subproblem 2
p + -6.666666665 = -374.892577206 Simplifying p + -6.666666665 = -374.892577206 Reorder the terms: -6.666666665 + p = -374.892577206 Solving -6.666666665 + p = -374.892577206 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '6.666666665' to each side of the equation. -6.666666665 + 6.666666665 + p = -374.892577206 + 6.666666665 Combine like terms: -6.666666665 + 6.666666665 = 0.000000000 0.000000000 + p = -374.892577206 + 6.666666665 p = -374.892577206 + 6.666666665 Combine like terms: -374.892577206 + 6.666666665 = -368.225910541 p = -368.225910541 Simplifying p = -368.225910541Solution
The solution to the problem is based on the solutions from the subproblems. p = {381.559243871, -368.225910541}
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