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Simplifying p2 + 10p = 13 Reorder the terms: 10p + p2 = 13 Solving 10p + p2 = 13 Solving for variable 'p'. Reorder the terms: -13 + 10p + p2 = 13 + -13 Combine like terms: 13 + -13 = 0 -13 + 10p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '13' to each side of the equation. -13 + 10p + 13 + p2 = 0 + 13 Reorder the terms: -13 + 13 + 10p + p2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + 10p + p2 = 0 + 13 10p + p2 = 0 + 13 Combine like terms: 0 + 13 = 13 10p + p2 = 13 The p term is 10p. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10p + 25 + p2 = 13 + 25 Reorder the terms: 25 + 10p + p2 = 13 + 25 Combine like terms: 13 + 25 = 38 25 + 10p + p2 = 38 Factor a perfect square on the left side: (p + 5)(p + 5) = 38 Calculate the square root of the right side: 6.164414003 Break this problem into two subproblems by setting (p + 5) equal to 6.164414003 and -6.164414003.Subproblem 1
p + 5 = 6.164414003 Simplifying p + 5 = 6.164414003 Reorder the terms: 5 + p = 6.164414003 Solving 5 + p = 6.164414003 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + p = 6.164414003 + -5 Combine like terms: 5 + -5 = 0 0 + p = 6.164414003 + -5 p = 6.164414003 + -5 Combine like terms: 6.164414003 + -5 = 1.164414003 p = 1.164414003 Simplifying p = 1.164414003Subproblem 2
p + 5 = -6.164414003 Simplifying p + 5 = -6.164414003 Reorder the terms: 5 + p = -6.164414003 Solving 5 + p = -6.164414003 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + p = -6.164414003 + -5 Combine like terms: 5 + -5 = 0 0 + p = -6.164414003 + -5 p = -6.164414003 + -5 Combine like terms: -6.164414003 + -5 = -11.164414003 p = -11.164414003 Simplifying p = -11.164414003Solution
The solution to the problem is based on the solutions from the subproblems. p = {1.164414003, -11.164414003}
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