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Simplifying 3p2 = 6p + 2 Reorder the terms: 3p2 = 2 + 6p Solving 3p2 = 2 + 6p Solving for variable 'p'. Reorder the terms: -2 + -6p + 3p2 = 2 + 6p + -2 + -6p Reorder the terms: -2 + -6p + 3p2 = 2 + -2 + 6p + -6p Combine like terms: 2 + -2 = 0 -2 + -6p + 3p2 = 0 + 6p + -6p -2 + -6p + 3p2 = 6p + -6p Combine like terms: 6p + -6p = 0 -2 + -6p + 3p2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -0.6666666667 + -2p + p2 = 0 Move the constant term to the right: Add '0.6666666667' to each side of the equation. -0.6666666667 + -2p + 0.6666666667 + p2 = 0 + 0.6666666667 Reorder the terms: -0.6666666667 + 0.6666666667 + -2p + p2 = 0 + 0.6666666667 Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000 0.0000000000 + -2p + p2 = 0 + 0.6666666667 -2p + p2 = 0 + 0.6666666667 Combine like terms: 0 + 0.6666666667 = 0.6666666667 -2p + p2 = 0.6666666667 The p term is -2p. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2p + 1 + p2 = 0.6666666667 + 1 Reorder the terms: 1 + -2p + p2 = 0.6666666667 + 1 Combine like terms: 0.6666666667 + 1 = 1.6666666667 1 + -2p + p2 = 1.6666666667 Factor a perfect square on the left side: (p + -1)(p + -1) = 1.6666666667 Calculate the square root of the right side: 1.290994449 Break this problem into two subproblems by setting (p + -1) equal to 1.290994449 and -1.290994449.Subproblem 1
p + -1 = 1.290994449 Simplifying p + -1 = 1.290994449 Reorder the terms: -1 + p = 1.290994449 Solving -1 + p = 1.290994449 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + p = 1.290994449 + 1 Combine like terms: -1 + 1 = 0 0 + p = 1.290994449 + 1 p = 1.290994449 + 1 Combine like terms: 1.290994449 + 1 = 2.290994449 p = 2.290994449 Simplifying p = 2.290994449Subproblem 2
p + -1 = -1.290994449 Simplifying p + -1 = -1.290994449 Reorder the terms: -1 + p = -1.290994449 Solving -1 + p = -1.290994449 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + p = -1.290994449 + 1 Combine like terms: -1 + 1 = 0 0 + p = -1.290994449 + 1 p = -1.290994449 + 1 Combine like terms: -1.290994449 + 1 = -0.290994449 p = -0.290994449 Simplifying p = -0.290994449Solution
The solution to the problem is based on the solutions from the subproblems. p = {2.290994449, -0.290994449}
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