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Simplifying 5p2 + 8p + -2 = 0 Reorder the terms: -2 + 8p + 5p2 = 0 Solving -2 + 8p + 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'. -0.4 + 1.6p + p2 = 0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + 1.6p + 0.4 + p2 = 0 + 0.4 Reorder the terms: -0.4 + 0.4 + 1.6p + p2 = 0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + 1.6p + p2 = 0 + 0.4 1.6p + p2 = 0 + 0.4 Combine like terms: 0 + 0.4 = 0.4 1.6p + p2 = 0.4 The p term is 1.6p. Take half its coefficient (0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. 1.6p + 0.64 + p2 = 0.4 + 0.64 Reorder the terms: 0.64 + 1.6p + p2 = 0.4 + 0.64 Combine like terms: 0.4 + 0.64 = 1.04 0.64 + 1.6p + p2 = 1.04 Factor a perfect square on the left side: (p + 0.8)(p + 0.8) = 1.04 Calculate the square root of the right side: 1.019803903 Break this problem into two subproblems by setting (p + 0.8) equal to 1.019803903 and -1.019803903.Subproblem 1
p + 0.8 = 1.019803903 Simplifying p + 0.8 = 1.019803903 Reorder the terms: 0.8 + p = 1.019803903 Solving 0.8 + p = 1.019803903 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + p = 1.019803903 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + p = 1.019803903 + -0.8 p = 1.019803903 + -0.8 Combine like terms: 1.019803903 + -0.8 = 0.219803903 p = 0.219803903 Simplifying p = 0.219803903Subproblem 2
p + 0.8 = -1.019803903 Simplifying p + 0.8 = -1.019803903 Reorder the terms: 0.8 + p = -1.019803903 Solving 0.8 + p = -1.019803903 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + p = -1.019803903 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + p = -1.019803903 + -0.8 p = -1.019803903 + -0.8 Combine like terms: -1.019803903 + -0.8 = -1.819803903 p = -1.819803903 Simplifying p = -1.819803903Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.219803903, -1.819803903}
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