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Simplifying 10n2 + -7n + -22 = 0 Reorder the terms: -22 + -7n + 10n2 = 0 Solving -22 + -7n + 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 + -0.7n + n2 = 0 Move the constant term to the right: Add '2.2' to each side of the equation. -2.2 + -0.7n + 2.2 + n2 = 0 + 2.2 Reorder the terms: -2.2 + 2.2 + -0.7n + n2 = 0 + 2.2 Combine like terms: -2.2 + 2.2 = 0.0 0.0 + -0.7n + n2 = 0 + 2.2 -0.7n + n2 = 0 + 2.2 Combine like terms: 0 + 2.2 = 2.2 -0.7n + n2 = 2.2 The n term is -0.7n. Take half its coefficient (-0.35). Square it (0.1225) and add it to both sides. Add '0.1225' to each side of the equation. -0.7n + 0.1225 + n2 = 2.2 + 0.1225 Reorder the terms: 0.1225 + -0.7n + n2 = 2.2 + 0.1225 Combine like terms: 2.2 + 0.1225 = 2.3225 0.1225 + -0.7n + n2 = 2.3225 Factor a perfect square on the left side: (n + -0.35)(n + -0.35) = 2.3225 Calculate the square root of the right side: 1.523975065 Break this problem into two subproblems by setting (n + -0.35) equal to 1.523975065 and -1.523975065.Subproblem 1
n + -0.35 = 1.523975065 Simplifying n + -0.35 = 1.523975065 Reorder the terms: -0.35 + n = 1.523975065 Solving -0.35 + n = 1.523975065 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.35' to each side of the equation. -0.35 + 0.35 + n = 1.523975065 + 0.35 Combine like terms: -0.35 + 0.35 = 0.00 0.00 + n = 1.523975065 + 0.35 n = 1.523975065 + 0.35 Combine like terms: 1.523975065 + 0.35 = 1.873975065 n = 1.873975065 Simplifying n = 1.873975065Subproblem 2
n + -0.35 = -1.523975065 Simplifying n + -0.35 = -1.523975065 Reorder the terms: -0.35 + n = -1.523975065 Solving -0.35 + n = -1.523975065 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.35' to each side of the equation. -0.35 + 0.35 + n = -1.523975065 + 0.35 Combine like terms: -0.35 + 0.35 = 0.00 0.00 + n = -1.523975065 + 0.35 n = -1.523975065 + 0.35 Combine like terms: -1.523975065 + 0.35 = -1.173975065 n = -1.173975065 Simplifying n = -1.173975065Solution
The solution to the problem is based on the solutions from the subproblems. n = {1.873975065, -1.173975065}
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