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Simplifying 10(n + -6) * n = 14 Reorder the terms: 10(-6 + n) * n = 14 Reorder the terms for easier multiplication: 10n(-6 + n) = 14 (-6 * 10n + n * 10n) = 14 (-60n + 10n2) = 14 Solving -60n + 10n2 = 14 Solving for variable 'n'. Reorder the terms: -14 + -60n + 10n2 = 14 + -14 Combine like terms: 14 + -14 = 0 -14 + -60n + 10n2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-7 + -30n + 5n2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-7 + -30n + 5n2)' equal to zero and attempt to solve: Simplifying -7 + -30n + 5n2 = 0 Solving -7 + -30n + 5n2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.4 + -6n + n2 = 0 Move the constant term to the right: Add '1.4' to each side of the equation. -1.4 + -6n + 1.4 + n2 = 0 + 1.4 Reorder the terms: -1.4 + 1.4 + -6n + n2 = 0 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + -6n + n2 = 0 + 1.4 -6n + n2 = 0 + 1.4 Combine like terms: 0 + 1.4 = 1.4 -6n + n2 = 1.4 The n term is -6n. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6n + 9 + n2 = 1.4 + 9 Reorder the terms: 9 + -6n + n2 = 1.4 + 9 Combine like terms: 1.4 + 9 = 10.4 9 + -6n + n2 = 10.4 Factor a perfect square on the left side: (n + -3)(n + -3) = 10.4 Calculate the square root of the right side: 3.224903099 Break this problem into two subproblems by setting (n + -3) equal to 3.224903099 and -3.224903099.Subproblem 1
n + -3 = 3.224903099 Simplifying n + -3 = 3.224903099 Reorder the terms: -3 + n = 3.224903099 Solving -3 + n = 3.224903099 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + n = 3.224903099 + 3 Combine like terms: -3 + 3 = 0 0 + n = 3.224903099 + 3 n = 3.224903099 + 3 Combine like terms: 3.224903099 + 3 = 6.224903099 n = 6.224903099 Simplifying n = 6.224903099Subproblem 2
n + -3 = -3.224903099 Simplifying n + -3 = -3.224903099 Reorder the terms: -3 + n = -3.224903099 Solving -3 + n = -3.224903099 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + n = -3.224903099 + 3 Combine like terms: -3 + 3 = 0 0 + n = -3.224903099 + 3 n = -3.224903099 + 3 Combine like terms: -3.224903099 + 3 = -0.224903099 n = -0.224903099 Simplifying n = -0.224903099Solution
The solution to the problem is based on the solutions from the subproblems. n = {6.224903099, -0.224903099}Solution
n = {6.224903099, -0.224903099}
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