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Simplifying 2 = 5p2 + -7p Reorder the terms: 2 = -7p + 5p2 Solving 2 = -7p + 5p2 Solving for variable 'p'. Reorder the terms: 2 + 7p + -5p2 = -7p + 7p + 5p2 + -5p2 Combine like terms: -7p + 7p = 0 2 + 7p + -5p2 = 0 + 5p2 + -5p2 2 + 7p + -5p2 = 5p2 + -5p2 Combine like terms: 5p2 + -5p2 = 0 2 + 7p + -5p2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -0.4 + -1.4p + p2 = 0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + -1.4p + 0.4 + p2 = 0 + 0.4 Reorder the terms: -0.4 + 0.4 + -1.4p + p2 = 0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + -1.4p + p2 = 0 + 0.4 -1.4p + p2 = 0 + 0.4 Combine like terms: 0 + 0.4 = 0.4 -1.4p + p2 = 0.4 The p term is -1.4p. Take half its coefficient (-0.7). Square it (0.49) and add it to both sides. Add '0.49' to each side of the equation. -1.4p + 0.49 + p2 = 0.4 + 0.49 Reorder the terms: 0.49 + -1.4p + p2 = 0.4 + 0.49 Combine like terms: 0.4 + 0.49 = 0.89 0.49 + -1.4p + p2 = 0.89 Factor a perfect square on the left side: (p + -0.7)(p + -0.7) = 0.89 Calculate the square root of the right side: 0.943398113 Break this problem into two subproblems by setting (p + -0.7) equal to 0.943398113 and -0.943398113.Subproblem 1
p + -0.7 = 0.943398113 Simplifying p + -0.7 = 0.943398113 Reorder the terms: -0.7 + p = 0.943398113 Solving -0.7 + p = 0.943398113 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + p = 0.943398113 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + p = 0.943398113 + 0.7 p = 0.943398113 + 0.7 Combine like terms: 0.943398113 + 0.7 = 1.643398113 p = 1.643398113 Simplifying p = 1.643398113Subproblem 2
p + -0.7 = -0.943398113 Simplifying p + -0.7 = -0.943398113 Reorder the terms: -0.7 + p = -0.943398113 Solving -0.7 + p = -0.943398113 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + p = -0.943398113 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + p = -0.943398113 + 0.7 p = -0.943398113 + 0.7 Combine like terms: -0.943398113 + 0.7 = -0.243398113 p = -0.243398113 Simplifying p = -0.243398113Solution
The solution to the problem is based on the solutions from the subproblems. p = {1.643398113, -0.243398113}
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