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Simplifying 2n2 + -16n + 7 = -8 Reorder the terms: 7 + -16n + 2n2 = -8 Solving 7 + -16n + 2n2 = -8 Solving for variable 'n'. Reorder the terms: 7 + 8 + -16n + 2n2 = -8 + 8 Combine like terms: 7 + 8 = 15 15 + -16n + 2n2 = -8 + 8 Combine like terms: -8 + 8 = 0 15 + -16n + 2n2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 7.5 + -8n + n2 = 0 Move the constant term to the right: Add '-7.5' to each side of the equation. 7.5 + -8n + -7.5 + n2 = 0 + -7.5 Reorder the terms: 7.5 + -7.5 + -8n + n2 = 0 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + -8n + n2 = 0 + -7.5 -8n + n2 = 0 + -7.5 Combine like terms: 0 + -7.5 = -7.5 -8n + n2 = -7.5 The n term is -8n. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8n + 16 + n2 = -7.5 + 16 Reorder the terms: 16 + -8n + n2 = -7.5 + 16 Combine like terms: -7.5 + 16 = 8.5 16 + -8n + n2 = 8.5 Factor a perfect square on the left side: (n + -4)(n + -4) = 8.5 Calculate the square root of the right side: 2.915475947 Break this problem into two subproblems by setting (n + -4) equal to 2.915475947 and -2.915475947.Subproblem 1
n + -4 = 2.915475947 Simplifying n + -4 = 2.915475947 Reorder the terms: -4 + n = 2.915475947 Solving -4 + n = 2.915475947 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + n = 2.915475947 + 4 Combine like terms: -4 + 4 = 0 0 + n = 2.915475947 + 4 n = 2.915475947 + 4 Combine like terms: 2.915475947 + 4 = 6.915475947 n = 6.915475947 Simplifying n = 6.915475947Subproblem 2
n + -4 = -2.915475947 Simplifying n + -4 = -2.915475947 Reorder the terms: -4 + n = -2.915475947 Solving -4 + n = -2.915475947 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + n = -2.915475947 + 4 Combine like terms: -4 + 4 = 0 0 + n = -2.915475947 + 4 n = -2.915475947 + 4 Combine like terms: -2.915475947 + 4 = 1.084524053 n = 1.084524053 Simplifying n = 1.084524053Solution
The solution to the problem is based on the solutions from the subproblems. n = {6.915475947, 1.084524053}
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