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Simplifying 10n2 + -2n + -7 = 0 Reorder the terms: -7 + -2n + 10n2 = 0 Solving -7 + -2n + 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'. -0.7 + -0.2n + n2 = 0 Move the constant term to the right: Add '0.7' to each side of the equation. -0.7 + -0.2n + 0.7 + n2 = 0 + 0.7 Reorder the terms: -0.7 + 0.7 + -0.2n + n2 = 0 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + -0.2n + n2 = 0 + 0.7 -0.2n + n2 = 0 + 0.7 Combine like terms: 0 + 0.7 = 0.7 -0.2n + n2 = 0.7 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 = 0.7 + 0.01 Reorder the terms: 0.01 + -0.2n + n2 = 0.7 + 0.01 Combine like terms: 0.7 + 0.01 = 0.71 0.01 + -0.2n + n2 = 0.71 Factor a perfect square on the left side: (n + -0.1)(n + -0.1) = 0.71 Calculate the square root of the right side: 0.842614977 Break this problem into two subproblems by setting (n + -0.1) equal to 0.842614977 and -0.842614977.Subproblem 1
n + -0.1 = 0.842614977 Simplifying n + -0.1 = 0.842614977 Reorder the terms: -0.1 + n = 0.842614977 Solving -0.1 + n = 0.842614977 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 = 0.842614977 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + n = 0.842614977 + 0.1 n = 0.842614977 + 0.1 Combine like terms: 0.842614977 + 0.1 = 0.942614977 n = 0.942614977 Simplifying n = 0.942614977Subproblem 2
n + -0.1 = -0.842614977 Simplifying n + -0.1 = -0.842614977 Reorder the terms: -0.1 + n = -0.842614977 Solving -0.1 + n = -0.842614977 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 = -0.842614977 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + n = -0.842614977 + 0.1 n = -0.842614977 + 0.1 Combine like terms: -0.842614977 + 0.1 = -0.742614977 n = -0.742614977 Simplifying n = -0.742614977Solution
The solution to the problem is based on the solutions from the subproblems. n = {0.942614977, -0.742614977}
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