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Simplifying 0 = -1p2 + 4p + 7 Reorder the terms: 0 = 7 + 4p + -1p2 Solving 0 = 7 + 4p + -1p2 Solving for variable 'p'. Combine like terms: 0 + -7 = -7 -7 + -4p + p2 = 7 + 4p + -1p2 + -7 + -4p + p2 Reorder the terms: -7 + -4p + p2 = 7 + -7 + 4p + -4p + -1p2 + p2 Combine like terms: 7 + -7 = 0 -7 + -4p + p2 = 0 + 4p + -4p + -1p2 + p2 -7 + -4p + p2 = 4p + -4p + -1p2 + p2 Combine like terms: 4p + -4p = 0 -7 + -4p + p2 = 0 + -1p2 + p2 -7 + -4p + p2 = -1p2 + p2 Combine like terms: -1p2 + p2 = 0 -7 + -4p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + -4p + 7 + p2 = 0 + 7 Reorder the terms: -7 + 7 + -4p + p2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -4p + p2 = 0 + 7 -4p + p2 = 0 + 7 Combine like terms: 0 + 7 = 7 -4p + p2 = 7 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 = 7 + 4 Reorder the terms: 4 + -4p + p2 = 7 + 4 Combine like terms: 7 + 4 = 11 4 + -4p + p2 = 11 Factor a perfect square on the left side: (p + -2)(p + -2) = 11 Calculate the square root of the right side: 3.31662479 Break this problem into two subproblems by setting (p + -2) equal to 3.31662479 and -3.31662479.Subproblem 1
p + -2 = 3.31662479 Simplifying p + -2 = 3.31662479 Reorder the terms: -2 + p = 3.31662479 Solving -2 + p = 3.31662479 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 = 3.31662479 + 2 Combine like terms: -2 + 2 = 0 0 + p = 3.31662479 + 2 p = 3.31662479 + 2 Combine like terms: 3.31662479 + 2 = 5.31662479 p = 5.31662479 Simplifying p = 5.31662479Subproblem 2
p + -2 = -3.31662479 Simplifying p + -2 = -3.31662479 Reorder the terms: -2 + p = -3.31662479 Solving -2 + p = -3.31662479 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 = -3.31662479 + 2 Combine like terms: -2 + 2 = 0 0 + p = -3.31662479 + 2 p = -3.31662479 + 2 Combine like terms: -3.31662479 + 2 = -1.31662479 p = -1.31662479 Simplifying p = -1.31662479Solution
The solution to the problem is based on the solutions from the subproblems. p = {5.31662479, -1.31662479}
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