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Simplifying -15n2 + 13 = -10n2 + -6n Reorder the terms: 13 + -15n2 = -10n2 + -6n Reorder the terms: 13 + -15n2 = -6n + -10n2 Solving 13 + -15n2 = -6n + -10n2 Solving for variable 'n'. Reorder the terms: 13 + 6n + -15n2 + 10n2 = -6n + -10n2 + 6n + 10n2 Combine like terms: -15n2 + 10n2 = -5n2 13 + 6n + -5n2 = -6n + -10n2 + 6n + 10n2 Reorder the terms: 13 + 6n + -5n2 = -6n + 6n + -10n2 + 10n2 Combine like terms: -6n + 6n = 0 13 + 6n + -5n2 = 0 + -10n2 + 10n2 13 + 6n + -5n2 = -10n2 + 10n2 Combine like terms: -10n2 + 10n2 = 0 13 + 6n + -5n2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -2.6 + -1.2n + n2 = 0 Move the constant term to the right: Add '2.6' to each side of the equation. -2.6 + -1.2n + 2.6 + n2 = 0 + 2.6 Reorder the terms: -2.6 + 2.6 + -1.2n + n2 = 0 + 2.6 Combine like terms: -2.6 + 2.6 = 0.0 0.0 + -1.2n + n2 = 0 + 2.6 -1.2n + n2 = 0 + 2.6 Combine like terms: 0 + 2.6 = 2.6 -1.2n + n2 = 2.6 The n term is -1.2n. Take half its coefficient (-0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. -1.2n + 0.36 + n2 = 2.6 + 0.36 Reorder the terms: 0.36 + -1.2n + n2 = 2.6 + 0.36 Combine like terms: 2.6 + 0.36 = 2.96 0.36 + -1.2n + n2 = 2.96 Factor a perfect square on the left side: (n + -0.6)(n + -0.6) = 2.96 Calculate the square root of the right side: 1.720465053 Break this problem into two subproblems by setting (n + -0.6) equal to 1.720465053 and -1.720465053.Subproblem 1
n + -0.6 = 1.720465053 Simplifying n + -0.6 = 1.720465053 Reorder the terms: -0.6 + n = 1.720465053 Solving -0.6 + n = 1.720465053 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + n = 1.720465053 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + n = 1.720465053 + 0.6 n = 1.720465053 + 0.6 Combine like terms: 1.720465053 + 0.6 = 2.320465053 n = 2.320465053 Simplifying n = 2.320465053Subproblem 2
n + -0.6 = -1.720465053 Simplifying n + -0.6 = -1.720465053 Reorder the terms: -0.6 + n = -1.720465053 Solving -0.6 + n = -1.720465053 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + n = -1.720465053 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + n = -1.720465053 + 0.6 n = -1.720465053 + 0.6 Combine like terms: -1.720465053 + 0.6 = -1.120465053 n = -1.120465053 Simplifying n = -1.120465053Solution
The solution to the problem is based on the solutions from the subproblems. n = {2.320465053, -1.120465053}
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