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Simplifying p2 + -15p = -21 Reorder the terms: -15p + p2 = -21 Solving -15p + p2 = -21 Solving for variable 'p'. Reorder the terms: 21 + -15p + p2 = -21 + 21 Combine like terms: -21 + 21 = 0 21 + -15p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '-21' to each side of the equation. 21 + -15p + -21 + p2 = 0 + -21 Reorder the terms: 21 + -21 + -15p + p2 = 0 + -21 Combine like terms: 21 + -21 = 0 0 + -15p + p2 = 0 + -21 -15p + p2 = 0 + -21 Combine like terms: 0 + -21 = -21 -15p + p2 = -21 The p term is -15p. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15p + 56.25 + p2 = -21 + 56.25 Reorder the terms: 56.25 + -15p + p2 = -21 + 56.25 Combine like terms: -21 + 56.25 = 35.25 56.25 + -15p + p2 = 35.25 Factor a perfect square on the left side: (p + -7.5)(p + -7.5) = 35.25 Calculate the square root of the right side: 5.937171044 Break this problem into two subproblems by setting (p + -7.5) equal to 5.937171044 and -5.937171044.Subproblem 1
p + -7.5 = 5.937171044 Simplifying p + -7.5 = 5.937171044 Reorder the terms: -7.5 + p = 5.937171044 Solving -7.5 + p = 5.937171044 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + p = 5.937171044 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + p = 5.937171044 + 7.5 p = 5.937171044 + 7.5 Combine like terms: 5.937171044 + 7.5 = 13.437171044 p = 13.437171044 Simplifying p = 13.437171044Subproblem 2
p + -7.5 = -5.937171044 Simplifying p + -7.5 = -5.937171044 Reorder the terms: -7.5 + p = -5.937171044 Solving -7.5 + p = -5.937171044 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + p = -5.937171044 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + p = -5.937171044 + 7.5 p = -5.937171044 + 7.5 Combine like terms: -5.937171044 + 7.5 = 1.562828956 p = 1.562828956 Simplifying p = 1.562828956Solution
The solution to the problem is based on the solutions from the subproblems. p = {13.437171044, 1.562828956}
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