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Simplifying p2 + 7p + -48 = 0 Reorder the terms: -48 + 7p + p2 = 0 Solving -48 + 7p + p2 = 0 Solving for variable 'p'. Begin completing the square. Move the constant term to the right: Add '48' to each side of the equation. -48 + 7p + 48 + p2 = 0 + 48 Reorder the terms: -48 + 48 + 7p + p2 = 0 + 48 Combine like terms: -48 + 48 = 0 0 + 7p + p2 = 0 + 48 7p + p2 = 0 + 48 Combine like terms: 0 + 48 = 48 7p + p2 = 48 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 = 48 + 12.25 Reorder the terms: 12.25 + 7p + p2 = 48 + 12.25 Combine like terms: 48 + 12.25 = 60.25 12.25 + 7p + p2 = 60.25 Factor a perfect square on the left side: (p + 3.5)(p + 3.5) = 60.25 Calculate the square root of the right side: 7.762087348 Break this problem into two subproblems by setting (p + 3.5) equal to 7.762087348 and -7.762087348.Subproblem 1
p + 3.5 = 7.762087348 Simplifying p + 3.5 = 7.762087348 Reorder the terms: 3.5 + p = 7.762087348 Solving 3.5 + p = 7.762087348 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 = 7.762087348 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + p = 7.762087348 + -3.5 p = 7.762087348 + -3.5 Combine like terms: 7.762087348 + -3.5 = 4.262087348 p = 4.262087348 Simplifying p = 4.262087348Subproblem 2
p + 3.5 = -7.762087348 Simplifying p + 3.5 = -7.762087348 Reorder the terms: 3.5 + p = -7.762087348 Solving 3.5 + p = -7.762087348 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 = -7.762087348 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + p = -7.762087348 + -3.5 p = -7.762087348 + -3.5 Combine like terms: -7.762087348 + -3.5 = -11.262087348 p = -11.262087348 Simplifying p = -11.262087348Solution
The solution to the problem is based on the solutions from the subproblems. p = {4.262087348, -11.262087348}
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