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Simplifying 5p2 + -2 = -4p Reorder the terms: -2 + 5p2 = -4p Solving -2 + 5p2 = -4p Solving for variable 'p'. Reorder the terms: -2 + 4p + 5p2 = -4p + 4p Combine like terms: -4p + 4p = 0 -2 + 4p + 5p2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.4 + 0.8p + p2 = 0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + 0.8p + 0.4 + p2 = 0 + 0.4 Reorder the terms: -0.4 + 0.4 + 0.8p + p2 = 0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + 0.8p + p2 = 0 + 0.4 0.8p + p2 = 0 + 0.4 Combine like terms: 0 + 0.4 = 0.4 0.8p + p2 = 0.4 The p term is 0.8p. Take half its coefficient (0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. 0.8p + 0.16 + p2 = 0.4 + 0.16 Reorder the terms: 0.16 + 0.8p + p2 = 0.4 + 0.16 Combine like terms: 0.4 + 0.16 = 0.56 0.16 + 0.8p + p2 = 0.56 Factor a perfect square on the left side: (p + 0.4)(p + 0.4) = 0.56 Calculate the square root of the right side: 0.748331477 Break this problem into two subproblems by setting (p + 0.4) equal to 0.748331477 and -0.748331477.Subproblem 1
p + 0.4 = 0.748331477 Simplifying p + 0.4 = 0.748331477 Reorder the terms: 0.4 + p = 0.748331477 Solving 0.4 + p = 0.748331477 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + p = 0.748331477 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + p = 0.748331477 + -0.4 p = 0.748331477 + -0.4 Combine like terms: 0.748331477 + -0.4 = 0.348331477 p = 0.348331477 Simplifying p = 0.348331477Subproblem 2
p + 0.4 = -0.748331477 Simplifying p + 0.4 = -0.748331477 Reorder the terms: 0.4 + p = -0.748331477 Solving 0.4 + p = -0.748331477 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + p = -0.748331477 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + p = -0.748331477 + -0.4 p = -0.748331477 + -0.4 Combine like terms: -0.748331477 + -0.4 = -1.148331477 p = -1.148331477 Simplifying p = -1.148331477Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.348331477, -1.148331477}
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