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Simplifying (8p2 + -5p) + -1(3p2 + -2p + 4) = 0 Reorder the terms: (-5p + 8p2) + -1(3p2 + -2p + 4) = 0 Remove parenthesis around (-5p + 8p2) -5p + 8p2 + -1(3p2 + -2p + 4) = 0 Reorder the terms: -5p + 8p2 + -1(4 + -2p + 3p2) = 0 -5p + 8p2 + (4 * -1 + -2p * -1 + 3p2 * -1) = 0 -5p + 8p2 + (-4 + 2p + -3p2) = 0 Reorder the terms: -4 + -5p + 2p + 8p2 + -3p2 = 0 Combine like terms: -5p + 2p = -3p -4 + -3p + 8p2 + -3p2 = 0 Combine like terms: 8p2 + -3p2 = 5p2 -4 + -3p + 5p2 = 0 Solving -4 + -3p + 5p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.8 + -0.6p + p2 = 0 Move the constant term to the right: Add '0.8' to each side of the equation. -0.8 + -0.6p + 0.8 + p2 = 0 + 0.8 Reorder the terms: -0.8 + 0.8 + -0.6p + p2 = 0 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + -0.6p + p2 = 0 + 0.8 -0.6p + p2 = 0 + 0.8 Combine like terms: 0 + 0.8 = 0.8 -0.6p + p2 = 0.8 The p term is -0.6p. Take half its coefficient (-0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. -0.6p + 0.09 + p2 = 0.8 + 0.09 Reorder the terms: 0.09 + -0.6p + p2 = 0.8 + 0.09 Combine like terms: 0.8 + 0.09 = 0.89 0.09 + -0.6p + p2 = 0.89 Factor a perfect square on the left side: (p + -0.3)(p + -0.3) = 0.89 Calculate the square root of the right side: 0.943398113 Break this problem into two subproblems by setting (p + -0.3) equal to 0.943398113 and -0.943398113.Subproblem 1
p + -0.3 = 0.943398113 Simplifying p + -0.3 = 0.943398113 Reorder the terms: -0.3 + p = 0.943398113 Solving -0.3 + p = 0.943398113 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + p = 0.943398113 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + p = 0.943398113 + 0.3 p = 0.943398113 + 0.3 Combine like terms: 0.943398113 + 0.3 = 1.243398113 p = 1.243398113 Simplifying p = 1.243398113Subproblem 2
p + -0.3 = -0.943398113 Simplifying p + -0.3 = -0.943398113 Reorder the terms: -0.3 + p = -0.943398113 Solving -0.3 + p = -0.943398113 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + p = -0.943398113 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + p = -0.943398113 + 0.3 p = -0.943398113 + 0.3 Combine like terms: -0.943398113 + 0.3 = -0.643398113 p = -0.643398113 Simplifying p = -0.643398113Solution
The solution to the problem is based on the solutions from the subproblems. p = {1.243398113, -0.643398113}
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