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Simplifying 0.02p2 + 2p + 20 = 0 Reorder the terms: 20 + 2p + 0.02p2 = 0 Solving 20 + 2p + 0.02p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by 0.02 the coefficient of the squared term: Divide each side by '0.02'. 1000 + 100p + p2 = 0 Move the constant term to the right: Add '-1000' to each side of the equation. 1000 + 100p + -1000 + p2 = 0 + -1000 Reorder the terms: 1000 + -1000 + 100p + p2 = 0 + -1000 Combine like terms: 1000 + -1000 = 0 0 + 100p + p2 = 0 + -1000 100p + p2 = 0 + -1000 Combine like terms: 0 + -1000 = -1000 100p + p2 = -1000 The p term is 100p. Take half its coefficient (50). Square it (2500) and add it to both sides. Add '2500' to each side of the equation. 100p + 2500 + p2 = -1000 + 2500 Reorder the terms: 2500 + 100p + p2 = -1000 + 2500 Combine like terms: -1000 + 2500 = 1500 2500 + 100p + p2 = 1500 Factor a perfect square on the left side: (p + 50)(p + 50) = 1500 Calculate the square root of the right side: 38.729833462 Break this problem into two subproblems by setting (p + 50) equal to 38.729833462 and -38.729833462.Subproblem 1
p + 50 = 38.729833462 Simplifying p + 50 = 38.729833462 Reorder the terms: 50 + p = 38.729833462 Solving 50 + p = 38.729833462 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-50' to each side of the equation. 50 + -50 + p = 38.729833462 + -50 Combine like terms: 50 + -50 = 0 0 + p = 38.729833462 + -50 p = 38.729833462 + -50 Combine like terms: 38.729833462 + -50 = -11.270166538 p = -11.270166538 Simplifying p = -11.270166538Subproblem 2
p + 50 = -38.729833462 Simplifying p + 50 = -38.729833462 Reorder the terms: 50 + p = -38.729833462 Solving 50 + p = -38.729833462 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-50' to each side of the equation. 50 + -50 + p = -38.729833462 + -50 Combine like terms: 50 + -50 = 0 0 + p = -38.729833462 + -50 p = -38.729833462 + -50 Combine like terms: -38.729833462 + -50 = -88.729833462 p = -88.729833462 Simplifying p = -88.729833462Solution
The solution to the problem is based on the solutions from the subproblems. p = {-11.270166538, -88.729833462}
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