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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 = 1.333333333 4 + -4p + p2 = 1.333333333 Factor a perfect square on the left side: (p + -2)(p + -2) = 1.333333333 Calculate the square root of the right side: 1.154700538 Break this problem into two subproblems by setting (p + -2) equal to 1.154700538 and -1.154700538.Subproblem 1
p + -2 = 1.154700538 Simplifying p + -2 = 1.154700538 Reorder the terms: -2 + p = 1.154700538 Solving -2 + p = 1.154700538 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 = 1.154700538 + 2 Combine like terms: -2 + 2 = 0 0 + p = 1.154700538 + 2 p = 1.154700538 + 2 Combine like terms: 1.154700538 + 2 = 3.154700538 p = 3.154700538 Simplifying p = 3.154700538Subproblem 2
p + -2 = -1.154700538 Simplifying p + -2 = -1.154700538 Reorder the terms: -2 + p = -1.154700538 Solving -2 + p = -1.154700538 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 = -1.154700538 + 2 Combine like terms: -2 + 2 = 0 0 + p = -1.154700538 + 2 p = -1.154700538 + 2 Combine like terms: -1.154700538 + 2 = 0.845299462 p = 0.845299462 Simplifying p = 0.845299462Solution
The solution to the problem is based on the solutions from the subproblems. p = {3.154700538, 0.845299462}
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