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Simplifying 10p2 + 9p = 3 Reorder the terms: 9p + 10p2 = 3 Solving 9p + 10p2 = 3 Solving for variable 'p'. Reorder the terms: -3 + 9p + 10p2 = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + 9p + 10p2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.3 + 0.9p + p2 = 0 Move the constant term to the right: Add '0.3' to each side of the equation. -0.3 + 0.9p + 0.3 + p2 = 0 + 0.3 Reorder the terms: -0.3 + 0.3 + 0.9p + p2 = 0 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + 0.9p + p2 = 0 + 0.3 0.9p + p2 = 0 + 0.3 Combine like terms: 0 + 0.3 = 0.3 0.9p + p2 = 0.3 The p term is 0.9p. Take half its coefficient (0.45). Square it (0.2025) and add it to both sides. Add '0.2025' to each side of the equation. 0.9p + 0.2025 + p2 = 0.3 + 0.2025 Reorder the terms: 0.2025 + 0.9p + p2 = 0.3 + 0.2025 Combine like terms: 0.3 + 0.2025 = 0.5025 0.2025 + 0.9p + p2 = 0.5025 Factor a perfect square on the left side: (p + 0.45)(p + 0.45) = 0.5025 Calculate the square root of the right side: 0.708872344 Break this problem into two subproblems by setting (p + 0.45) equal to 0.708872344 and -0.708872344.Subproblem 1
p + 0.45 = 0.708872344 Simplifying p + 0.45 = 0.708872344 Reorder the terms: 0.45 + p = 0.708872344 Solving 0.45 + p = 0.708872344 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.45' to each side of the equation. 0.45 + -0.45 + p = 0.708872344 + -0.45 Combine like terms: 0.45 + -0.45 = 0.00 0.00 + p = 0.708872344 + -0.45 p = 0.708872344 + -0.45 Combine like terms: 0.708872344 + -0.45 = 0.258872344 p = 0.258872344 Simplifying p = 0.258872344Subproblem 2
p + 0.45 = -0.708872344 Simplifying p + 0.45 = -0.708872344 Reorder the terms: 0.45 + p = -0.708872344 Solving 0.45 + p = -0.708872344 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.45' to each side of the equation. 0.45 + -0.45 + p = -0.708872344 + -0.45 Combine like terms: 0.45 + -0.45 = 0.00 0.00 + p = -0.708872344 + -0.45 p = -0.708872344 + -0.45 Combine like terms: -0.708872344 + -0.45 = -1.158872344 p = -1.158872344 Simplifying p = -1.158872344Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.258872344, -1.158872344}
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