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Simplifying p2 + -7p = 28 Reorder the terms: -7p + p2 = 28 Solving -7p + p2 = 28 Solving for variable 'p'. Reorder the terms: -28 + -7p + p2 = 28 + -28 Combine like terms: 28 + -28 = 0 -28 + -7p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '28' to each side of the equation. -28 + -7p + 28 + p2 = 0 + 28 Reorder the terms: -28 + 28 + -7p + p2 = 0 + 28 Combine like terms: -28 + 28 = 0 0 + -7p + p2 = 0 + 28 -7p + p2 = 0 + 28 Combine like terms: 0 + 28 = 28 -7p + p2 = 28 The p term is -7p. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7p + 12.25 + p2 = 28 + 12.25 Reorder the terms: 12.25 + -7p + p2 = 28 + 12.25 Combine like terms: 28 + 12.25 = 40.25 12.25 + -7p + p2 = 40.25 Factor a perfect square on the left side: (p + -3.5)(p + -3.5) = 40.25 Calculate the square root of the right side: 6.34428877 Break this problem into two subproblems by setting (p + -3.5) equal to 6.34428877 and -6.34428877.Subproblem 1
p + -3.5 = 6.34428877 Simplifying p + -3.5 = 6.34428877 Reorder the terms: -3.5 + p = 6.34428877 Solving -3.5 + p = 6.34428877 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + p = 6.34428877 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + p = 6.34428877 + 3.5 p = 6.34428877 + 3.5 Combine like terms: 6.34428877 + 3.5 = 9.84428877 p = 9.84428877 Simplifying p = 9.84428877Subproblem 2
p + -3.5 = -6.34428877 Simplifying p + -3.5 = -6.34428877 Reorder the terms: -3.5 + p = -6.34428877 Solving -3.5 + p = -6.34428877 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + p = -6.34428877 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + p = -6.34428877 + 3.5 p = -6.34428877 + 3.5 Combine like terms: -6.34428877 + 3.5 = -2.84428877 p = -2.84428877 Simplifying p = -2.84428877Solution
The solution to the problem is based on the solutions from the subproblems. p = {9.84428877, -2.84428877}
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