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Simplifying 4n2 + -2n + -7 = 0 Reorder the terms: -7 + -2n + 4n2 = 0 Solving -7 + -2n + 4n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.75 + -0.5n + n2 = 0 Move the constant term to the right: Add '1.75' to each side of the equation. -1.75 + -0.5n + 1.75 + n2 = 0 + 1.75 Reorder the terms: -1.75 + 1.75 + -0.5n + n2 = 0 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + -0.5n + n2 = 0 + 1.75 -0.5n + n2 = 0 + 1.75 Combine like terms: 0 + 1.75 = 1.75 -0.5n + n2 = 1.75 The n term is -0.5n. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5n + 0.0625 + n2 = 1.75 + 0.0625 Reorder the terms: 0.0625 + -0.5n + n2 = 1.75 + 0.0625 Combine like terms: 1.75 + 0.0625 = 1.8125 0.0625 + -0.5n + n2 = 1.8125 Factor a perfect square on the left side: (n + -0.25)(n + -0.25) = 1.8125 Calculate the square root of the right side: 1.346291202 Break this problem into two subproblems by setting (n + -0.25) equal to 1.346291202 and -1.346291202.Subproblem 1
n + -0.25 = 1.346291202 Simplifying n + -0.25 = 1.346291202 Reorder the terms: -0.25 + n = 1.346291202 Solving -0.25 + n = 1.346291202 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + n = 1.346291202 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + n = 1.346291202 + 0.25 n = 1.346291202 + 0.25 Combine like terms: 1.346291202 + 0.25 = 1.596291202 n = 1.596291202 Simplifying n = 1.596291202Subproblem 2
n + -0.25 = -1.346291202 Simplifying n + -0.25 = -1.346291202 Reorder the terms: -0.25 + n = -1.346291202 Solving -0.25 + n = -1.346291202 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + n = -1.346291202 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + n = -1.346291202 + 0.25 n = -1.346291202 + 0.25 Combine like terms: -1.346291202 + 0.25 = -1.096291202 n = -1.096291202 Simplifying n = -1.096291202Solution
The solution to the problem is based on the solutions from the subproblems. n = {1.596291202, -1.096291202}
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