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Simplifying (-8n2 + 7n + -5) + -1(-7n2 + 2) = 0 Reorder the terms: (-5 + 7n + -8n2) + -1(-7n2 + 2) = 0 Remove parenthesis around (-5 + 7n + -8n2) -5 + 7n + -8n2 + -1(-7n2 + 2) = 0 Reorder the terms: -5 + 7n + -8n2 + -1(2 + -7n2) = 0 -5 + 7n + -8n2 + (2 * -1 + -7n2 * -1) = 0 -5 + 7n + -8n2 + (-2 + 7n2) = 0 Reorder the terms: -5 + -2 + 7n + -8n2 + 7n2 = 0 Combine like terms: -5 + -2 = -7 -7 + 7n + -8n2 + 7n2 = 0 Combine like terms: -8n2 + 7n2 = -1n2 -7 + 7n + -1n2 = 0 Solving -7 + 7n + -1n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 7 + -7n + n2 = 0 Move the constant term to the right: Add '-7' to each side of the equation. 7 + -7n + -7 + n2 = 0 + -7 Reorder the terms: 7 + -7 + -7n + n2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -7n + n2 = 0 + -7 -7n + n2 = 0 + -7 Combine like terms: 0 + -7 = -7 -7n + n2 = -7 The n term is -7n. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7n + 12.25 + n2 = -7 + 12.25 Reorder the terms: 12.25 + -7n + n2 = -7 + 12.25 Combine like terms: -7 + 12.25 = 5.25 12.25 + -7n + n2 = 5.25 Factor a perfect square on the left side: (n + -3.5)(n + -3.5) = 5.25 Calculate the square root of the right side: 2.291287847 Break this problem into two subproblems by setting (n + -3.5) equal to 2.291287847 and -2.291287847.Subproblem 1
n + -3.5 = 2.291287847 Simplifying n + -3.5 = 2.291287847 Reorder the terms: -3.5 + n = 2.291287847 Solving -3.5 + n = 2.291287847 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + n = 2.291287847 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + n = 2.291287847 + 3.5 n = 2.291287847 + 3.5 Combine like terms: 2.291287847 + 3.5 = 5.791287847 n = 5.791287847 Simplifying n = 5.791287847Subproblem 2
n + -3.5 = -2.291287847 Simplifying n + -3.5 = -2.291287847 Reorder the terms: -3.5 + n = -2.291287847 Solving -3.5 + n = -2.291287847 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + n = -2.291287847 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + n = -2.291287847 + 3.5 n = -2.291287847 + 3.5 Combine like terms: -2.291287847 + 3.5 = 1.208712153 n = 1.208712153 Simplifying n = 1.208712153Solution
The solution to the problem is based on the solutions from the subproblems. n = {5.791287847, 1.208712153}
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