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Simplifying p2 + -4p + -54 = 0 Reorder the terms: -54 + -4p + p2 = 0 Solving -54 + -4p + p2 = 0 Solving for variable 'p'. Begin completing the square. Move the constant term to the right: Add '54' to each side of the equation. -54 + -4p + 54 + p2 = 0 + 54 Reorder the terms: -54 + 54 + -4p + p2 = 0 + 54 Combine like terms: -54 + 54 = 0 0 + -4p + p2 = 0 + 54 -4p + p2 = 0 + 54 Combine like terms: 0 + 54 = 54 -4p + p2 = 54 The p term is -4p. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4p + 4 + p2 = 54 + 4 Reorder the terms: 4 + -4p + p2 = 54 + 4 Combine like terms: 54 + 4 = 58 4 + -4p + p2 = 58 Factor a perfect square on the left side: (p + -2)(p + -2) = 58 Calculate the square root of the right side: 7.615773106 Break this problem into two subproblems by setting (p + -2) equal to 7.615773106 and -7.615773106.Subproblem 1
p + -2 = 7.615773106 Simplifying p + -2 = 7.615773106 Reorder the terms: -2 + p = 7.615773106 Solving -2 + p = 7.615773106 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + p = 7.615773106 + 2 Combine like terms: -2 + 2 = 0 0 + p = 7.615773106 + 2 p = 7.615773106 + 2 Combine like terms: 7.615773106 + 2 = 9.615773106 p = 9.615773106 Simplifying p = 9.615773106Subproblem 2
p + -2 = -7.615773106 Simplifying p + -2 = -7.615773106 Reorder the terms: -2 + p = -7.615773106 Solving -2 + p = -7.615773106 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + p = -7.615773106 + 2 Combine like terms: -2 + 2 = 0 0 + p = -7.615773106 + 2 p = -7.615773106 + 2 Combine like terms: -7.615773106 + 2 = -5.615773106 p = -5.615773106 Simplifying p = -5.615773106Solution
The solution to the problem is based on the solutions from the subproblems. p = {9.615773106, -5.615773106}
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