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Simplifying p2 + 14p + 15 = 0 Reorder the terms: 15 + 14p + p2 = 0 Solving 15 + 14p + p2 = 0 Solving for variable 'p'. Begin completing the square. Move the constant term to the right: Add '-15' to each side of the equation. 15 + 14p + -15 + p2 = 0 + -15 Reorder the terms: 15 + -15 + 14p + p2 = 0 + -15 Combine like terms: 15 + -15 = 0 0 + 14p + p2 = 0 + -15 14p + p2 = 0 + -15 Combine like terms: 0 + -15 = -15 14p + p2 = -15 The p term is 14p. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14p + 49 + p2 = -15 + 49 Reorder the terms: 49 + 14p + p2 = -15 + 49 Combine like terms: -15 + 49 = 34 49 + 14p + p2 = 34 Factor a perfect square on the left side: (p + 7)(p + 7) = 34 Calculate the square root of the right side: 5.830951895 Break this problem into two subproblems by setting (p + 7) equal to 5.830951895 and -5.830951895.Subproblem 1
p + 7 = 5.830951895 Simplifying p + 7 = 5.830951895 Reorder the terms: 7 + p = 5.830951895 Solving 7 + p = 5.830951895 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + p = 5.830951895 + -7 Combine like terms: 7 + -7 = 0 0 + p = 5.830951895 + -7 p = 5.830951895 + -7 Combine like terms: 5.830951895 + -7 = -1.169048105 p = -1.169048105 Simplifying p = -1.169048105Subproblem 2
p + 7 = -5.830951895 Simplifying p + 7 = -5.830951895 Reorder the terms: 7 + p = -5.830951895 Solving 7 + p = -5.830951895 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + p = -5.830951895 + -7 Combine like terms: 7 + -7 = 0 0 + p = -5.830951895 + -7 p = -5.830951895 + -7 Combine like terms: -5.830951895 + -7 = -12.830951895 p = -12.830951895 Simplifying p = -12.830951895Solution
The solution to the problem is based on the solutions from the subproblems. p = {-1.169048105, -12.830951895}
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