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Simplifying 5n2 + 10n = 7 Reorder the terms: 10n + 5n2 = 7 Solving 10n + 5n2 = 7 Solving for variable 'n'. Reorder the terms: -7 + 10n + 5n2 = 7 + -7 Combine like terms: 7 + -7 = 0 -7 + 10n + 5n2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.4 + 2n + n2 = 0 Move the constant term to the right: Add '1.4' to each side of the equation. -1.4 + 2n + 1.4 + n2 = 0 + 1.4 Reorder the terms: -1.4 + 1.4 + 2n + n2 = 0 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + 2n + n2 = 0 + 1.4 2n + n2 = 0 + 1.4 Combine like terms: 0 + 1.4 = 1.4 2n + n2 = 1.4 The n term is 2n. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2n + 1 + n2 = 1.4 + 1 Reorder the terms: 1 + 2n + n2 = 1.4 + 1 Combine like terms: 1.4 + 1 = 2.4 1 + 2n + n2 = 2.4 Factor a perfect square on the left side: (n + 1)(n + 1) = 2.4 Calculate the square root of the right side: 1.549193338 Break this problem into two subproblems by setting (n + 1) equal to 1.549193338 and -1.549193338.Subproblem 1
n + 1 = 1.549193338 Simplifying n + 1 = 1.549193338 Reorder the terms: 1 + n = 1.549193338 Solving 1 + n = 1.549193338 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + n = 1.549193338 + -1 Combine like terms: 1 + -1 = 0 0 + n = 1.549193338 + -1 n = 1.549193338 + -1 Combine like terms: 1.549193338 + -1 = 0.549193338 n = 0.549193338 Simplifying n = 0.549193338Subproblem 2
n + 1 = -1.549193338 Simplifying n + 1 = -1.549193338 Reorder the terms: 1 + n = -1.549193338 Solving 1 + n = -1.549193338 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + n = -1.549193338 + -1 Combine like terms: 1 + -1 = 0 0 + n = -1.549193338 + -1 n = -1.549193338 + -1 Combine like terms: -1.549193338 + -1 = -2.549193338 n = -2.549193338 Simplifying n = -2.549193338Solution
The solution to the problem is based on the solutions from the subproblems. n = {0.549193338, -2.549193338}
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