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Simplifying 4n2 + 8n + -15 = 0 Reorder the terms: -15 + 8n + 4n2 = 0 Solving -15 + 8n + 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'. -3.75 + 2n + n2 = 0 Move the constant term to the right: Add '3.75' to each side of the equation. -3.75 + 2n + 3.75 + n2 = 0 + 3.75 Reorder the terms: -3.75 + 3.75 + 2n + n2 = 0 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + 2n + n2 = 0 + 3.75 2n + n2 = 0 + 3.75 Combine like terms: 0 + 3.75 = 3.75 2n + n2 = 3.75 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 = 3.75 + 1 Reorder the terms: 1 + 2n + n2 = 3.75 + 1 Combine like terms: 3.75 + 1 = 4.75 1 + 2n + n2 = 4.75 Factor a perfect square on the left side: (n + 1)(n + 1) = 4.75 Calculate the square root of the right side: 2.179449472 Break this problem into two subproblems by setting (n + 1) equal to 2.179449472 and -2.179449472.Subproblem 1
n + 1 = 2.179449472 Simplifying n + 1 = 2.179449472 Reorder the terms: 1 + n = 2.179449472 Solving 1 + n = 2.179449472 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 = 2.179449472 + -1 Combine like terms: 1 + -1 = 0 0 + n = 2.179449472 + -1 n = 2.179449472 + -1 Combine like terms: 2.179449472 + -1 = 1.179449472 n = 1.179449472 Simplifying n = 1.179449472Subproblem 2
n + 1 = -2.179449472 Simplifying n + 1 = -2.179449472 Reorder the terms: 1 + n = -2.179449472 Solving 1 + n = -2.179449472 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 = -2.179449472 + -1 Combine like terms: 1 + -1 = 0 0 + n = -2.179449472 + -1 n = -2.179449472 + -1 Combine like terms: -2.179449472 + -1 = -3.179449472 n = -3.179449472 Simplifying n = -3.179449472Solution
The solution to the problem is based on the solutions from the subproblems. n = {1.179449472, -3.179449472}
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