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Simplifying 10n2 + -2n + -2 = 0 Reorder the terms: -2 + -2n + 10n2 = 0 Solving -2 + -2n + 10n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + -1n + 5n2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + -1n + 5n2)' equal to zero and attempt to solve: Simplifying -1 + -1n + 5n2 = 0 Solving -1 + -1n + 5n2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.2 + -0.2n + n2 = 0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + -0.2n + 0.2 + n2 = 0 + 0.2 Reorder the terms: -0.2 + 0.2 + -0.2n + n2 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + -0.2n + n2 = 0 + 0.2 -0.2n + n2 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 -0.2n + n2 = 0.2 The n term is -0.2n. Take half its coefficient (-0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. -0.2n + 0.01 + n2 = 0.2 + 0.01 Reorder the terms: 0.01 + -0.2n + n2 = 0.2 + 0.01 Combine like terms: 0.2 + 0.01 = 0.21 0.01 + -0.2n + n2 = 0.21 Factor a perfect square on the left side: (n + -0.1)(n + -0.1) = 0.21 Calculate the square root of the right side: 0.458257569 Break this problem into two subproblems by setting (n + -0.1) equal to 0.458257569 and -0.458257569.Subproblem 1
n + -0.1 = 0.458257569 Simplifying n + -0.1 = 0.458257569 Reorder the terms: -0.1 + n = 0.458257569 Solving -0.1 + n = 0.458257569 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + n = 0.458257569 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + n = 0.458257569 + 0.1 n = 0.458257569 + 0.1 Combine like terms: 0.458257569 + 0.1 = 0.558257569 n = 0.558257569 Simplifying n = 0.558257569Subproblem 2
n + -0.1 = -0.458257569 Simplifying n + -0.1 = -0.458257569 Reorder the terms: -0.1 + n = -0.458257569 Solving -0.1 + n = -0.458257569 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + n = -0.458257569 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + n = -0.458257569 + 0.1 n = -0.458257569 + 0.1 Combine like terms: -0.458257569 + 0.1 = -0.358257569 n = -0.358257569 Simplifying n = -0.358257569Solution
The solution to the problem is based on the solutions from the subproblems. n = {0.558257569, -0.358257569}Solution
n = {0.558257569, -0.358257569}
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