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Simplifying p2 + -6p + -34 = 0 Reorder the terms: -34 + -6p + p2 = 0 Solving -34 + -6p + p2 = 0 Solving for variable 'p'. Begin completing the square. Move the constant term to the right: Add '34' to each side of the equation. -34 + -6p + 34 + p2 = 0 + 34 Reorder the terms: -34 + 34 + -6p + p2 = 0 + 34 Combine like terms: -34 + 34 = 0 0 + -6p + p2 = 0 + 34 -6p + p2 = 0 + 34 Combine like terms: 0 + 34 = 34 -6p + p2 = 34 The p term is -6p. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6p + 9 + p2 = 34 + 9 Reorder the terms: 9 + -6p + p2 = 34 + 9 Combine like terms: 34 + 9 = 43 9 + -6p + p2 = 43 Factor a perfect square on the left side: (p + -3)(p + -3) = 43 Calculate the square root of the right side: 6.557438524 Break this problem into two subproblems by setting (p + -3) equal to 6.557438524 and -6.557438524.Subproblem 1
p + -3 = 6.557438524 Simplifying p + -3 = 6.557438524 Reorder the terms: -3 + p = 6.557438524 Solving -3 + p = 6.557438524 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + p = 6.557438524 + 3 Combine like terms: -3 + 3 = 0 0 + p = 6.557438524 + 3 p = 6.557438524 + 3 Combine like terms: 6.557438524 + 3 = 9.557438524 p = 9.557438524 Simplifying p = 9.557438524Subproblem 2
p + -3 = -6.557438524 Simplifying p + -3 = -6.557438524 Reorder the terms: -3 + p = -6.557438524 Solving -3 + p = -6.557438524 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + p = -6.557438524 + 3 Combine like terms: -3 + 3 = 0 0 + p = -6.557438524 + 3 p = -6.557438524 + 3 Combine like terms: -6.557438524 + 3 = -3.557438524 p = -3.557438524 Simplifying p = -3.557438524Solution
The solution to the problem is based on the solutions from the subproblems. p = {9.557438524, -3.557438524}
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