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Simplifying p2 + -12p + -19 = 0 Reorder the terms: -19 + -12p + p2 = 0 Solving -19 + -12p + p2 = 0 Solving for variable 'p'. Begin completing the square. Move the constant term to the right: Add '19' to each side of the equation. -19 + -12p + 19 + p2 = 0 + 19 Reorder the terms: -19 + 19 + -12p + p2 = 0 + 19 Combine like terms: -19 + 19 = 0 0 + -12p + p2 = 0 + 19 -12p + p2 = 0 + 19 Combine like terms: 0 + 19 = 19 -12p + p2 = 19 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 = 19 + 36 Reorder the terms: 36 + -12p + p2 = 19 + 36 Combine like terms: 19 + 36 = 55 36 + -12p + p2 = 55 Factor a perfect square on the left side: (p + -6)(p + -6) = 55 Calculate the square root of the right side: 7.416198487 Break this problem into two subproblems by setting (p + -6) equal to 7.416198487 and -7.416198487.Subproblem 1
p + -6 = 7.416198487 Simplifying p + -6 = 7.416198487 Reorder the terms: -6 + p = 7.416198487 Solving -6 + p = 7.416198487 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 = 7.416198487 + 6 Combine like terms: -6 + 6 = 0 0 + p = 7.416198487 + 6 p = 7.416198487 + 6 Combine like terms: 7.416198487 + 6 = 13.416198487 p = 13.416198487 Simplifying p = 13.416198487Subproblem 2
p + -6 = -7.416198487 Simplifying p + -6 = -7.416198487 Reorder the terms: -6 + p = -7.416198487 Solving -6 + p = -7.416198487 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 = -7.416198487 + 6 Combine like terms: -6 + 6 = 0 0 + p = -7.416198487 + 6 p = -7.416198487 + 6 Combine like terms: -7.416198487 + 6 = -1.416198487 p = -1.416198487 Simplifying p = -1.416198487Solution
The solution to the problem is based on the solutions from the subproblems. p = {13.416198487, -1.416198487}
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