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Simplifying -3p2 + -12p + 8 = 0 Reorder the terms: 8 + -12p + -3p2 = 0 Solving 8 + -12p + -3p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -2.666666667 + 4p + p2 = 0 Move the constant term to the right: Add '2.666666667' to each side of the equation. -2.666666667 + 4p + 2.666666667 + p2 = 0 + 2.666666667 Reorder the terms: -2.666666667 + 2.666666667 + 4p + p2 = 0 + 2.666666667 Combine like terms: -2.666666667 + 2.666666667 = 0.000000000 0.000000000 + 4p + p2 = 0 + 2.666666667 4p + p2 = 0 + 2.666666667 Combine like terms: 0 + 2.666666667 = 2.666666667 4p + p2 = 2.666666667 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 = 2.666666667 + 4 Reorder the terms: 4 + 4p + p2 = 2.666666667 + 4 Combine like terms: 2.666666667 + 4 = 6.666666667 4 + 4p + p2 = 6.666666667 Factor a perfect square on the left side: (p + 2)(p + 2) = 6.666666667 Calculate the square root of the right side: 2.581988898 Break this problem into two subproblems by setting (p + 2) equal to 2.581988898 and -2.581988898.Subproblem 1
p + 2 = 2.581988898 Simplifying p + 2 = 2.581988898 Reorder the terms: 2 + p = 2.581988898 Solving 2 + p = 2.581988898 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 = 2.581988898 + -2 Combine like terms: 2 + -2 = 0 0 + p = 2.581988898 + -2 p = 2.581988898 + -2 Combine like terms: 2.581988898 + -2 = 0.581988898 p = 0.581988898 Simplifying p = 0.581988898Subproblem 2
p + 2 = -2.581988898 Simplifying p + 2 = -2.581988898 Reorder the terms: 2 + p = -2.581988898 Solving 2 + p = -2.581988898 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 = -2.581988898 + -2 Combine like terms: 2 + -2 = 0 0 + p = -2.581988898 + -2 p = -2.581988898 + -2 Combine like terms: -2.581988898 + -2 = -4.581988898 p = -4.581988898 Simplifying p = -4.581988898Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.581988898, -4.581988898}
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