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Simplifying 10n2 + -7 = -4n Reorder the terms: -7 + 10n2 = -4n Solving -7 + 10n2 = -4n Solving for variable 'n'. Reorder the terms: -7 + 4n + 10n2 = -4n + 4n Combine like terms: -4n + 4n = 0 -7 + 4n + 10n2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.7 + 0.4n + n2 = 0 Move the constant term to the right: Add '0.7' to each side of the equation. -0.7 + 0.4n + 0.7 + n2 = 0 + 0.7 Reorder the terms: -0.7 + 0.7 + 0.4n + n2 = 0 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + 0.4n + n2 = 0 + 0.7 0.4n + n2 = 0 + 0.7 Combine like terms: 0 + 0.7 = 0.7 0.4n + n2 = 0.7 The n term is 0.4n. Take half its coefficient (0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. 0.4n + 0.04 + n2 = 0.7 + 0.04 Reorder the terms: 0.04 + 0.4n + n2 = 0.7 + 0.04 Combine like terms: 0.7 + 0.04 = 0.74 0.04 + 0.4n + n2 = 0.74 Factor a perfect square on the left side: (n + 0.2)(n + 0.2) = 0.74 Calculate the square root of the right side: 0.860232527 Break this problem into two subproblems by setting (n + 0.2) equal to 0.860232527 and -0.860232527.Subproblem 1
n + 0.2 = 0.860232527 Simplifying n + 0.2 = 0.860232527 Reorder the terms: 0.2 + n = 0.860232527 Solving 0.2 + n = 0.860232527 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + n = 0.860232527 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + n = 0.860232527 + -0.2 n = 0.860232527 + -0.2 Combine like terms: 0.860232527 + -0.2 = 0.660232527 n = 0.660232527 Simplifying n = 0.660232527Subproblem 2
n + 0.2 = -0.860232527 Simplifying n + 0.2 = -0.860232527 Reorder the terms: 0.2 + n = -0.860232527 Solving 0.2 + n = -0.860232527 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + n = -0.860232527 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + n = -0.860232527 + -0.2 n = -0.860232527 + -0.2 Combine like terms: -0.860232527 + -0.2 = -1.060232527 n = -1.060232527 Simplifying n = -1.060232527Solution
The solution to the problem is based on the solutions from the subproblems. n = {0.660232527, -1.060232527}
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