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Simplifying 4n2 + -10 = 5n Reorder the terms: -10 + 4n2 = 5n Solving -10 + 4n2 = 5n Solving for variable 'n'. Reorder the terms: -10 + -5n + 4n2 = 5n + -5n Combine like terms: 5n + -5n = 0 -10 + -5n + 4n2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -2.5 + -1.25n + n2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + -1.25n + 2.5 + n2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + -1.25n + n2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + -1.25n + n2 = 0 + 2.5 -1.25n + n2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 -1.25n + n2 = 2.5 The n term is -1.25n. Take half its coefficient (-0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. -1.25n + 0.390625 + n2 = 2.5 + 0.390625 Reorder the terms: 0.390625 + -1.25n + n2 = 2.5 + 0.390625 Combine like terms: 2.5 + 0.390625 = 2.890625 0.390625 + -1.25n + n2 = 2.890625 Factor a perfect square on the left side: (n + -0.625)(n + -0.625) = 2.890625 Calculate the square root of the right side: 1.700183814 Break this problem into two subproblems by setting (n + -0.625) equal to 1.700183814 and -1.700183814.Subproblem 1
n + -0.625 = 1.700183814 Simplifying n + -0.625 = 1.700183814 Reorder the terms: -0.625 + n = 1.700183814 Solving -0.625 + n = 1.700183814 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + n = 1.700183814 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + n = 1.700183814 + 0.625 n = 1.700183814 + 0.625 Combine like terms: 1.700183814 + 0.625 = 2.325183814 n = 2.325183814 Simplifying n = 2.325183814Subproblem 2
n + -0.625 = -1.700183814 Simplifying n + -0.625 = -1.700183814 Reorder the terms: -0.625 + n = -1.700183814 Solving -0.625 + n = -1.700183814 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + n = -1.700183814 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + n = -1.700183814 + 0.625 n = -1.700183814 + 0.625 Combine like terms: -1.700183814 + 0.625 = -1.075183814 n = -1.075183814 Simplifying n = -1.075183814Solution
The solution to the problem is based on the solutions from the subproblems. n = {2.325183814, -1.075183814}
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