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Simplifying p2 + 26p + -19 = 0 Reorder the terms: -19 + 26p + p2 = 0 Solving -19 + 26p + 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 + 26p + 19 + p2 = 0 + 19 Reorder the terms: -19 + 19 + 26p + p2 = 0 + 19 Combine like terms: -19 + 19 = 0 0 + 26p + p2 = 0 + 19 26p + p2 = 0 + 19 Combine like terms: 0 + 19 = 19 26p + p2 = 19 The p term is 26p. Take half its coefficient (13). Square it (169) and add it to both sides. Add '169' to each side of the equation. 26p + 169 + p2 = 19 + 169 Reorder the terms: 169 + 26p + p2 = 19 + 169 Combine like terms: 19 + 169 = 188 169 + 26p + p2 = 188 Factor a perfect square on the left side: (p + 13)(p + 13) = 188 Calculate the square root of the right side: 13.711309201 Break this problem into two subproblems by setting (p + 13) equal to 13.711309201 and -13.711309201.Subproblem 1
p + 13 = 13.711309201 Simplifying p + 13 = 13.711309201 Reorder the terms: 13 + p = 13.711309201 Solving 13 + p = 13.711309201 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + p = 13.711309201 + -13 Combine like terms: 13 + -13 = 0 0 + p = 13.711309201 + -13 p = 13.711309201 + -13 Combine like terms: 13.711309201 + -13 = 0.711309201 p = 0.711309201 Simplifying p = 0.711309201Subproblem 2
p + 13 = -13.711309201 Simplifying p + 13 = -13.711309201 Reorder the terms: 13 + p = -13.711309201 Solving 13 + p = -13.711309201 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + p = -13.711309201 + -13 Combine like terms: 13 + -13 = 0 0 + p = -13.711309201 + -13 p = -13.711309201 + -13 Combine like terms: -13.711309201 + -13 = -26.711309201 p = -26.711309201 Simplifying p = -26.711309201Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.711309201, -26.711309201}
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