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Simplifying 8n2 + 8n + -17 = 7 Reorder the terms: -17 + 8n + 8n2 = 7 Solving -17 + 8n + 8n2 = 7 Solving for variable 'n'. Reorder the terms: -17 + -7 + 8n + 8n2 = 7 + -7 Combine like terms: -17 + -7 = -24 -24 + 8n + 8n2 = 7 + -7 Combine like terms: 7 + -7 = 0 -24 + 8n + 8n2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(-3 + n + n2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(-3 + n + n2)' equal to zero and attempt to solve: Simplifying -3 + n + n2 = 0 Solving -3 + n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + n + 3 + n2 = 0 + 3 Reorder the terms: -3 + 3 + n + n2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + n + n2 = 0 + 3 n + n2 = 0 + 3 Combine like terms: 0 + 3 = 3 n + n2 = 3 The n term is n. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. n + 0.25 + n2 = 3 + 0.25 Reorder the terms: 0.25 + n + n2 = 3 + 0.25 Combine like terms: 3 + 0.25 = 3.25 0.25 + n + n2 = 3.25 Factor a perfect square on the left side: (n + 0.5)(n + 0.5) = 3.25 Calculate the square root of the right side: 1.802775638 Break this problem into two subproblems by setting (n + 0.5) equal to 1.802775638 and -1.802775638.Subproblem 1
n + 0.5 = 1.802775638 Simplifying n + 0.5 = 1.802775638 Reorder the terms: 0.5 + n = 1.802775638 Solving 0.5 + n = 1.802775638 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + n = 1.802775638 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = 1.802775638 + -0.5 n = 1.802775638 + -0.5 Combine like terms: 1.802775638 + -0.5 = 1.302775638 n = 1.302775638 Simplifying n = 1.302775638Subproblem 2
n + 0.5 = -1.802775638 Simplifying n + 0.5 = -1.802775638 Reorder the terms: 0.5 + n = -1.802775638 Solving 0.5 + n = -1.802775638 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + n = -1.802775638 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = -1.802775638 + -0.5 n = -1.802775638 + -0.5 Combine like terms: -1.802775638 + -0.5 = -2.302775638 n = -2.302775638 Simplifying n = -2.302775638Solution
The solution to the problem is based on the solutions from the subproblems. n = {1.302775638, -2.302775638}Solution
n = {1.302775638, -2.302775638}
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