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Simplifying 10n2 + -11n + -22 = 0 Reorder the terms: -22 + -11n + 10n2 = 0 Solving -22 + -11n + 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'. -2.2 + -1.1n + n2 = 0 Move the constant term to the right: Add '2.2' to each side of the equation. -2.2 + -1.1n + 2.2 + n2 = 0 + 2.2 Reorder the terms: -2.2 + 2.2 + -1.1n + n2 = 0 + 2.2 Combine like terms: -2.2 + 2.2 = 0.0 0.0 + -1.1n + n2 = 0 + 2.2 -1.1n + n2 = 0 + 2.2 Combine like terms: 0 + 2.2 = 2.2 -1.1n + n2 = 2.2 The n term is -1.1n. Take half its coefficient (-0.55). Square it (0.3025) and add it to both sides. Add '0.3025' to each side of the equation. -1.1n + 0.3025 + n2 = 2.2 + 0.3025 Reorder the terms: 0.3025 + -1.1n + n2 = 2.2 + 0.3025 Combine like terms: 2.2 + 0.3025 = 2.5025 0.3025 + -1.1n + n2 = 2.5025 Factor a perfect square on the left side: (n + -0.55)(n + -0.55) = 2.5025 Calculate the square root of the right side: 1.581929202 Break this problem into two subproblems by setting (n + -0.55) equal to 1.581929202 and -1.581929202.Subproblem 1
n + -0.55 = 1.581929202 Simplifying n + -0.55 = 1.581929202 Reorder the terms: -0.55 + n = 1.581929202 Solving -0.55 + n = 1.581929202 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.55' to each side of the equation. -0.55 + 0.55 + n = 1.581929202 + 0.55 Combine like terms: -0.55 + 0.55 = 0.00 0.00 + n = 1.581929202 + 0.55 n = 1.581929202 + 0.55 Combine like terms: 1.581929202 + 0.55 = 2.131929202 n = 2.131929202 Simplifying n = 2.131929202Subproblem 2
n + -0.55 = -1.581929202 Simplifying n + -0.55 = -1.581929202 Reorder the terms: -0.55 + n = -1.581929202 Solving -0.55 + n = -1.581929202 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.55' to each side of the equation. -0.55 + 0.55 + n = -1.581929202 + 0.55 Combine like terms: -0.55 + 0.55 = 0.00 0.00 + n = -1.581929202 + 0.55 n = -1.581929202 + 0.55 Combine like terms: -1.581929202 + 0.55 = -1.031929202 n = -1.031929202 Simplifying n = -1.031929202Solution
The solution to the problem is based on the solutions from the subproblems. n = {2.131929202, -1.031929202}
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