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Simplifying 10n2 + -6n + -21 = 0 Reorder the terms: -21 + -6n + 10n2 = 0 Solving -21 + -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'. -2.1 + -0.6n + n2 = 0 Move the constant term to the right: Add '2.1' to each side of the equation. -2.1 + -0.6n + 2.1 + n2 = 0 + 2.1 Reorder the terms: -2.1 + 2.1 + -0.6n + n2 = 0 + 2.1 Combine like terms: -2.1 + 2.1 = 0.0 0.0 + -0.6n + n2 = 0 + 2.1 -0.6n + n2 = 0 + 2.1 Combine like terms: 0 + 2.1 = 2.1 -0.6n + n2 = 2.1 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 = 2.1 + 0.09 Reorder the terms: 0.09 + -0.6n + n2 = 2.1 + 0.09 Combine like terms: 2.1 + 0.09 = 2.19 0.09 + -0.6n + n2 = 2.19 Factor a perfect square on the left side: (n + -0.3)(n + -0.3) = 2.19 Calculate the square root of the right side: 1.479864859 Break this problem into two subproblems by setting (n + -0.3) equal to 1.479864859 and -1.479864859.Subproblem 1
n + -0.3 = 1.479864859 Simplifying n + -0.3 = 1.479864859 Reorder the terms: -0.3 + n = 1.479864859 Solving -0.3 + n = 1.479864859 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 = 1.479864859 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + n = 1.479864859 + 0.3 n = 1.479864859 + 0.3 Combine like terms: 1.479864859 + 0.3 = 1.779864859 n = 1.779864859 Simplifying n = 1.779864859Subproblem 2
n + -0.3 = -1.479864859 Simplifying n + -0.3 = -1.479864859 Reorder the terms: -0.3 + n = -1.479864859 Solving -0.3 + n = -1.479864859 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 = -1.479864859 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + n = -1.479864859 + 0.3 n = -1.479864859 + 0.3 Combine like terms: -1.479864859 + 0.3 = -1.179864859 n = -1.179864859 Simplifying n = -1.179864859Solution
The solution to the problem is based on the solutions from the subproblems. n = {1.779864859, -1.179864859}
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