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Simplifying 10p2 + 9p + -45 = 0 Reorder the terms: -45 + 9p + 10p2 = 0 Solving -45 + 9p + 10p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -4.5 + 0.9p + p2 = 0 Move the constant term to the right: Add '4.5' to each side of the equation. -4.5 + 0.9p + 4.5 + p2 = 0 + 4.5 Reorder the terms: -4.5 + 4.5 + 0.9p + p2 = 0 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + 0.9p + p2 = 0 + 4.5 0.9p + p2 = 0 + 4.5 Combine like terms: 0 + 4.5 = 4.5 0.9p + p2 = 4.5 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 = 4.5 + 0.2025 Reorder the terms: 0.2025 + 0.9p + p2 = 4.5 + 0.2025 Combine like terms: 4.5 + 0.2025 = 4.7025 0.2025 + 0.9p + p2 = 4.7025 Factor a perfect square on the left side: (p + 0.45)(p + 0.45) = 4.7025 Calculate the square root of the right side: 2.168524844 Break this problem into two subproblems by setting (p + 0.45) equal to 2.168524844 and -2.168524844.Subproblem 1
p + 0.45 = 2.168524844 Simplifying p + 0.45 = 2.168524844 Reorder the terms: 0.45 + p = 2.168524844 Solving 0.45 + p = 2.168524844 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 = 2.168524844 + -0.45 Combine like terms: 0.45 + -0.45 = 0.00 0.00 + p = 2.168524844 + -0.45 p = 2.168524844 + -0.45 Combine like terms: 2.168524844 + -0.45 = 1.718524844 p = 1.718524844 Simplifying p = 1.718524844Subproblem 2
p + 0.45 = -2.168524844 Simplifying p + 0.45 = -2.168524844 Reorder the terms: 0.45 + p = -2.168524844 Solving 0.45 + p = -2.168524844 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 = -2.168524844 + -0.45 Combine like terms: 0.45 + -0.45 = 0.00 0.00 + p = -2.168524844 + -0.45 p = -2.168524844 + -0.45 Combine like terms: -2.168524844 + -0.45 = -2.618524844 p = -2.618524844 Simplifying p = -2.618524844Solution
The solution to the problem is based on the solutions from the subproblems. p = {1.718524844, -2.618524844}
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