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Simplifying 0.5p2 = 4p + -8 Reorder the terms: 0.5p2 = -8 + 4p Solving 0.5p2 = -8 + 4p Solving for variable 'p'. Reorder the terms: 8 + -4p + 0.5p2 = -8 + 4p + 8 + -4p Reorder the terms: 8 + -4p + 0.5p2 = -8 + 8 + 4p + -4p Combine like terms: -8 + 8 = 0 8 + -4p + 0.5p2 = 0 + 4p + -4p 8 + -4p + 0.5p2 = 4p + -4p Combine like terms: 4p + -4p = 0 8 + -4p + 0.5p2 = 0 Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. 16 + -8p + p2 = 0 Move the constant term to the right: Add '-16' to each side of the equation. 16 + -8p + -16 + p2 = 0 + -16 Reorder the terms: 16 + -16 + -8p + p2 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + -8p + p2 = 0 + -16 -8p + p2 = 0 + -16 Combine like terms: 0 + -16 = -16 -8p + p2 = -16 The p term is -8p. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8p + 16 + p2 = -16 + 16 Reorder the terms: 16 + -8p + p2 = -16 + 16 Combine like terms: -16 + 16 = 0 16 + -8p + p2 = 0 Factor a perfect square on the left side: (p + -4)(p + -4) = 0 Calculate the square root of the right side: 0 Break this problem into two subproblems by setting (p + -4) equal to 0 and 0.Subproblem 1
p + -4 = 0 Simplifying p + -4 = 0 Reorder the terms: -4 + p = 0 Solving -4 + p = 0 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + p = 0 + 4 Combine like terms: -4 + 4 = 0 0 + p = 0 + 4 p = 0 + 4 Combine like terms: 0 + 4 = 4 p = 4 Simplifying p = 4Subproblem 2
p + -4 = 0 Simplifying p + -4 = 0 Reorder the terms: -4 + p = 0 Solving -4 + p = 0 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + p = 0 + 4 Combine like terms: -4 + 4 = 0 0 + p = 0 + 4 p = 0 + 4 Combine like terms: 0 + 4 = 4 p = 4 Simplifying p = 4Solution
The solution to the problem is based on the solutions from the subproblems. p = {4, 4}
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