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Simplifying 5n2 + -4n + -10 = 15 Reorder the terms: -10 + -4n + 5n2 = 15 Solving -10 + -4n + 5n2 = 15 Solving for variable 'n'. Reorder the terms: -10 + -15 + -4n + 5n2 = 15 + -15 Combine like terms: -10 + -15 = -25 -25 + -4n + 5n2 = 15 + -15 Combine like terms: 15 + -15 = 0 -25 + -4n + 5n2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -5 + -0.8n + n2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + -0.8n + 5 + n2 = 0 + 5 Reorder the terms: -5 + 5 + -0.8n + n2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -0.8n + n2 = 0 + 5 -0.8n + n2 = 0 + 5 Combine like terms: 0 + 5 = 5 -0.8n + n2 = 5 The n term is -0.8n. Take half its coefficient (-0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. -0.8n + 0.16 + n2 = 5 + 0.16 Reorder the terms: 0.16 + -0.8n + n2 = 5 + 0.16 Combine like terms: 5 + 0.16 = 5.16 0.16 + -0.8n + n2 = 5.16 Factor a perfect square on the left side: (n + -0.4)(n + -0.4) = 5.16 Calculate the square root of the right side: 2.271563338 Break this problem into two subproblems by setting (n + -0.4) equal to 2.271563338 and -2.271563338.Subproblem 1
n + -0.4 = 2.271563338 Simplifying n + -0.4 = 2.271563338 Reorder the terms: -0.4 + n = 2.271563338 Solving -0.4 + n = 2.271563338 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + n = 2.271563338 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + n = 2.271563338 + 0.4 n = 2.271563338 + 0.4 Combine like terms: 2.271563338 + 0.4 = 2.671563338 n = 2.671563338 Simplifying n = 2.671563338Subproblem 2
n + -0.4 = -2.271563338 Simplifying n + -0.4 = -2.271563338 Reorder the terms: -0.4 + n = -2.271563338 Solving -0.4 + n = -2.271563338 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + n = -2.271563338 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + n = -2.271563338 + 0.4 n = -2.271563338 + 0.4 Combine like terms: -2.271563338 + 0.4 = -1.871563338 n = -1.871563338 Simplifying n = -1.871563338Solution
The solution to the problem is based on the solutions from the subproblems. n = {2.671563338, -1.871563338}
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