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Simplifying 8n2 + -16n + -7 = 0 Reorder the terms: -7 + -16n + 8n2 = 0 Solving -7 + -16n + 8n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.875 + -2n + n2 = 0 Move the constant term to the right: Add '0.875' to each side of the equation. -0.875 + -2n + 0.875 + n2 = 0 + 0.875 Reorder the terms: -0.875 + 0.875 + -2n + n2 = 0 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + -2n + n2 = 0 + 0.875 -2n + n2 = 0 + 0.875 Combine like terms: 0 + 0.875 = 0.875 -2n + n2 = 0.875 The n term is -2n. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2n + 1 + n2 = 0.875 + 1 Reorder the terms: 1 + -2n + n2 = 0.875 + 1 Combine like terms: 0.875 + 1 = 1.875 1 + -2n + n2 = 1.875 Factor a perfect square on the left side: (n + -1)(n + -1) = 1.875 Calculate the square root of the right side: 1.369306394 Break this problem into two subproblems by setting (n + -1) equal to 1.369306394 and -1.369306394.Subproblem 1
n + -1 = 1.369306394 Simplifying n + -1 = 1.369306394 Reorder the terms: -1 + n = 1.369306394 Solving -1 + n = 1.369306394 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + n = 1.369306394 + 1 Combine like terms: -1 + 1 = 0 0 + n = 1.369306394 + 1 n = 1.369306394 + 1 Combine like terms: 1.369306394 + 1 = 2.369306394 n = 2.369306394 Simplifying n = 2.369306394Subproblem 2
n + -1 = -1.369306394 Simplifying n + -1 = -1.369306394 Reorder the terms: -1 + n = -1.369306394 Solving -1 + n = -1.369306394 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + n = -1.369306394 + 1 Combine like terms: -1 + 1 = 0 0 + n = -1.369306394 + 1 n = -1.369306394 + 1 Combine like terms: -1.369306394 + 1 = -0.369306394 n = -0.369306394 Simplifying n = -0.369306394Solution
The solution to the problem is based on the solutions from the subproblems. n = {2.369306394, -0.369306394}
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