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Simplifying 3p2 + -1p + 7 = 4p2 + 3p + -1 Reorder the terms: 7 + -1p + 3p2 = 4p2 + 3p + -1 Reorder the terms: 7 + -1p + 3p2 = -1 + 3p + 4p2 Solving 7 + -1p + 3p2 = -1 + 3p + 4p2 Solving for variable 'p'. Reorder the terms: 7 + 1 + -1p + -3p + 3p2 + -4p2 = -1 + 3p + 4p2 + 1 + -3p + -4p2 Combine like terms: 7 + 1 = 8 8 + -1p + -3p + 3p2 + -4p2 = -1 + 3p + 4p2 + 1 + -3p + -4p2 Combine like terms: -1p + -3p = -4p 8 + -4p + 3p2 + -4p2 = -1 + 3p + 4p2 + 1 + -3p + -4p2 Combine like terms: 3p2 + -4p2 = -1p2 8 + -4p + -1p2 = -1 + 3p + 4p2 + 1 + -3p + -4p2 Reorder the terms: 8 + -4p + -1p2 = -1 + 1 + 3p + -3p + 4p2 + -4p2 Combine like terms: -1 + 1 = 0 8 + -4p + -1p2 = 0 + 3p + -3p + 4p2 + -4p2 8 + -4p + -1p2 = 3p + -3p + 4p2 + -4p2 Combine like terms: 3p + -3p = 0 8 + -4p + -1p2 = 0 + 4p2 + -4p2 8 + -4p + -1p2 = 4p2 + -4p2 Combine like terms: 4p2 + -4p2 = 0 8 + -4p + -1p2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -8 + 4p + p2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + 4p + 8 + p2 = 0 + 8 Reorder the terms: -8 + 8 + 4p + p2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 4p + p2 = 0 + 8 4p + p2 = 0 + 8 Combine like terms: 0 + 8 = 8 4p + p2 = 8 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 = 8 + 4 Reorder the terms: 4 + 4p + p2 = 8 + 4 Combine like terms: 8 + 4 = 12 4 + 4p + p2 = 12 Factor a perfect square on the left side: (p + 2)(p + 2) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (p + 2) equal to 3.464101615 and -3.464101615.Subproblem 1
p + 2 = 3.464101615 Simplifying p + 2 = 3.464101615 Reorder the terms: 2 + p = 3.464101615 Solving 2 + p = 3.464101615 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 = 3.464101615 + -2 Combine like terms: 2 + -2 = 0 0 + p = 3.464101615 + -2 p = 3.464101615 + -2 Combine like terms: 3.464101615 + -2 = 1.464101615 p = 1.464101615 Simplifying p = 1.464101615Subproblem 2
p + 2 = -3.464101615 Simplifying p + 2 = -3.464101615 Reorder the terms: 2 + p = -3.464101615 Solving 2 + p = -3.464101615 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 = -3.464101615 + -2 Combine like terms: 2 + -2 = 0 0 + p = -3.464101615 + -2 p = -3.464101615 + -2 Combine like terms: -3.464101615 + -2 = -5.464101615 p = -5.464101615 Simplifying p = -5.464101615Solution
The solution to the problem is based on the solutions from the subproblems. p = {1.464101615, -5.464101615}
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