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Simplifying 5p2 = 6p + 3 Reorder the terms: 5p2 = 3 + 6p Solving 5p2 = 3 + 6p Solving for variable 'p'. Reorder the terms: -3 + -6p + 5p2 = 3 + 6p + -3 + -6p Reorder the terms: -3 + -6p + 5p2 = 3 + -3 + 6p + -6p Combine like terms: 3 + -3 = 0 -3 + -6p + 5p2 = 0 + 6p + -6p -3 + -6p + 5p2 = 6p + -6p Combine like terms: 6p + -6p = 0 -3 + -6p + 5p2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.6 + -1.2p + p2 = 0 Move the constant term to the right: Add '0.6' to each side of the equation. -0.6 + -1.2p + 0.6 + p2 = 0 + 0.6 Reorder the terms: -0.6 + 0.6 + -1.2p + p2 = 0 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + -1.2p + p2 = 0 + 0.6 -1.2p + p2 = 0 + 0.6 Combine like terms: 0 + 0.6 = 0.6 -1.2p + p2 = 0.6 The p term is -1.2p. Take half its coefficient (-0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. -1.2p + 0.36 + p2 = 0.6 + 0.36 Reorder the terms: 0.36 + -1.2p + p2 = 0.6 + 0.36 Combine like terms: 0.6 + 0.36 = 0.96 0.36 + -1.2p + p2 = 0.96 Factor a perfect square on the left side: (p + -0.6)(p + -0.6) = 0.96 Calculate the square root of the right side: 0.979795897 Break this problem into two subproblems by setting (p + -0.6) equal to 0.979795897 and -0.979795897.Subproblem 1
p + -0.6 = 0.979795897 Simplifying p + -0.6 = 0.979795897 Reorder the terms: -0.6 + p = 0.979795897 Solving -0.6 + p = 0.979795897 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + p = 0.979795897 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + p = 0.979795897 + 0.6 p = 0.979795897 + 0.6 Combine like terms: 0.979795897 + 0.6 = 1.579795897 p = 1.579795897 Simplifying p = 1.579795897Subproblem 2
p + -0.6 = -0.979795897 Simplifying p + -0.6 = -0.979795897 Reorder the terms: -0.6 + p = -0.979795897 Solving -0.6 + p = -0.979795897 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + p = -0.979795897 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + p = -0.979795897 + 0.6 p = -0.979795897 + 0.6 Combine like terms: -0.979795897 + 0.6 = -0.379795897 p = -0.379795897 Simplifying p = -0.379795897Solution
The solution to the problem is based on the solutions from the subproblems. p = {1.579795897, -0.379795897}
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