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Simplifying p2 + 60p + -600 = 0 Reorder the terms: -600 + 60p + p2 = 0 Solving -600 + 60p + p2 = 0 Solving for variable 'p'. Begin completing the square. Move the constant term to the right: Add '600' to each side of the equation. -600 + 60p + 600 + p2 = 0 + 600 Reorder the terms: -600 + 600 + 60p + p2 = 0 + 600 Combine like terms: -600 + 600 = 0 0 + 60p + p2 = 0 + 600 60p + p2 = 0 + 600 Combine like terms: 0 + 600 = 600 60p + p2 = 600 The p term is 60p. Take half its coefficient (30). Square it (900) and add it to both sides. Add '900' to each side of the equation. 60p + 900 + p2 = 600 + 900 Reorder the terms: 900 + 60p + p2 = 600 + 900 Combine like terms: 600 + 900 = 1500 900 + 60p + p2 = 1500 Factor a perfect square on the left side: (p + 30)(p + 30) = 1500 Calculate the square root of the right side: 38.729833462 Break this problem into two subproblems by setting (p + 30) equal to 38.729833462 and -38.729833462.Subproblem 1
p + 30 = 38.729833462 Simplifying p + 30 = 38.729833462 Reorder the terms: 30 + p = 38.729833462 Solving 30 + p = 38.729833462 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-30' to each side of the equation. 30 + -30 + p = 38.729833462 + -30 Combine like terms: 30 + -30 = 0 0 + p = 38.729833462 + -30 p = 38.729833462 + -30 Combine like terms: 38.729833462 + -30 = 8.729833462 p = 8.729833462 Simplifying p = 8.729833462Subproblem 2
p + 30 = -38.729833462 Simplifying p + 30 = -38.729833462 Reorder the terms: 30 + p = -38.729833462 Solving 30 + p = -38.729833462 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-30' to each side of the equation. 30 + -30 + p = -38.729833462 + -30 Combine like terms: 30 + -30 = 0 0 + p = -38.729833462 + -30 p = -38.729833462 + -30 Combine like terms: -38.729833462 + -30 = -68.729833462 p = -68.729833462 Simplifying p = -68.729833462Solution
The solution to the problem is based on the solutions from the subproblems. p = {8.729833462, -68.729833462}
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