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Simplifying 10n2 + 6n + -3 = 0 Reorder the terms: -3 + 6n + 10n2 = 0 Solving -3 + 6n + 10n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.3 + 0.6n + n2 = 0 Move the constant term to the right: Add '0.3' to each side of the equation. -0.3 + 0.6n + 0.3 + n2 = 0 + 0.3 Reorder the terms: -0.3 + 0.3 + 0.6n + n2 = 0 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + 0.6n + n2 = 0 + 0.3 0.6n + n2 = 0 + 0.3 Combine like terms: 0 + 0.3 = 0.3 0.6n + n2 = 0.3 The n term is 0.6n. Take half its coefficient (0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. 0.6n + 0.09 + n2 = 0.3 + 0.09 Reorder the terms: 0.09 + 0.6n + n2 = 0.3 + 0.09 Combine like terms: 0.3 + 0.09 = 0.39 0.09 + 0.6n + n2 = 0.39 Factor a perfect square on the left side: (n + 0.3)(n + 0.3) = 0.39 Calculate the square root of the right side: 0.6244998 Break this problem into two subproblems by setting (n + 0.3) equal to 0.6244998 and -0.6244998.Subproblem 1
n + 0.3 = 0.6244998 Simplifying n + 0.3 = 0.6244998 Reorder the terms: 0.3 + n = 0.6244998 Solving 0.3 + n = 0.6244998 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + n = 0.6244998 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + n = 0.6244998 + -0.3 n = 0.6244998 + -0.3 Combine like terms: 0.6244998 + -0.3 = 0.3244998 n = 0.3244998 Simplifying n = 0.3244998Subproblem 2
n + 0.3 = -0.6244998 Simplifying n + 0.3 = -0.6244998 Reorder the terms: 0.3 + n = -0.6244998 Solving 0.3 + n = -0.6244998 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + n = -0.6244998 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + n = -0.6244998 + -0.3 n = -0.6244998 + -0.3 Combine like terms: -0.6244998 + -0.3 = -0.9244998 n = -0.9244998 Simplifying n = -0.9244998Solution
The solution to the problem is based on the solutions from the subproblems. n = {0.3244998, -0.9244998}
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