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Simplifying p2 + -12p + 36 = 80 Reorder the terms: 36 + -12p + p2 = 80 Solving 36 + -12p + p2 = 80 Solving for variable 'p'. Reorder the terms: 36 + -80 + -12p + p2 = 80 + -80 Combine like terms: 36 + -80 = -44 -44 + -12p + p2 = 80 + -80 Combine like terms: 80 + -80 = 0 -44 + -12p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '44' to each side of the equation. -44 + -12p + 44 + p2 = 0 + 44 Reorder the terms: -44 + 44 + -12p + p2 = 0 + 44 Combine like terms: -44 + 44 = 0 0 + -12p + p2 = 0 + 44 -12p + p2 = 0 + 44 Combine like terms: 0 + 44 = 44 -12p + p2 = 44 The p term is -12p. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12p + 36 + p2 = 44 + 36 Reorder the terms: 36 + -12p + p2 = 44 + 36 Combine like terms: 44 + 36 = 80 36 + -12p + p2 = 80 Factor a perfect square on the left side: (p + -6)(p + -6) = 80 Calculate the square root of the right side: 8.94427191 Break this problem into two subproblems by setting (p + -6) equal to 8.94427191 and -8.94427191.Subproblem 1
p + -6 = 8.94427191 Simplifying p + -6 = 8.94427191 Reorder the terms: -6 + p = 8.94427191 Solving -6 + p = 8.94427191 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + p = 8.94427191 + 6 Combine like terms: -6 + 6 = 0 0 + p = 8.94427191 + 6 p = 8.94427191 + 6 Combine like terms: 8.94427191 + 6 = 14.94427191 p = 14.94427191 Simplifying p = 14.94427191Subproblem 2
p + -6 = -8.94427191 Simplifying p + -6 = -8.94427191 Reorder the terms: -6 + p = -8.94427191 Solving -6 + p = -8.94427191 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + p = -8.94427191 + 6 Combine like terms: -6 + 6 = 0 0 + p = -8.94427191 + 6 p = -8.94427191 + 6 Combine like terms: -8.94427191 + 6 = -2.94427191 p = -2.94427191 Simplifying p = -2.94427191Solution
The solution to the problem is based on the solutions from the subproblems. p = {14.94427191, -2.94427191}
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