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Simplifying p2 + -6p + -49 = 0 Reorder the terms: -49 + -6p + p2 = 0 Solving -49 + -6p + p2 = 0 Solving for variable 'p'. Begin completing the square. Move the constant term to the right: Add '49' to each side of the equation. -49 + -6p + 49 + p2 = 0 + 49 Reorder the terms: -49 + 49 + -6p + p2 = 0 + 49 Combine like terms: -49 + 49 = 0 0 + -6p + p2 = 0 + 49 -6p + p2 = 0 + 49 Combine like terms: 0 + 49 = 49 -6p + p2 = 49 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 = 49 + 9 Reorder the terms: 9 + -6p + p2 = 49 + 9 Combine like terms: 49 + 9 = 58 9 + -6p + p2 = 58 Factor a perfect square on the left side: (p + -3)(p + -3) = 58 Calculate the square root of the right side: 7.615773106 Break this problem into two subproblems by setting (p + -3) equal to 7.615773106 and -7.615773106.Subproblem 1
p + -3 = 7.615773106 Simplifying p + -3 = 7.615773106 Reorder the terms: -3 + p = 7.615773106 Solving -3 + p = 7.615773106 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 = 7.615773106 + 3 Combine like terms: -3 + 3 = 0 0 + p = 7.615773106 + 3 p = 7.615773106 + 3 Combine like terms: 7.615773106 + 3 = 10.615773106 p = 10.615773106 Simplifying p = 10.615773106Subproblem 2
p + -3 = -7.615773106 Simplifying p + -3 = -7.615773106 Reorder the terms: -3 + p = -7.615773106 Solving -3 + p = -7.615773106 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 = -7.615773106 + 3 Combine like terms: -3 + 3 = 0 0 + p = -7.615773106 + 3 p = -7.615773106 + 3 Combine like terms: -7.615773106 + 3 = -4.615773106 p = -4.615773106 Simplifying p = -4.615773106Solution
The solution to the problem is based on the solutions from the subproblems. p = {10.615773106, -4.615773106}
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