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Simplifying 7n2 + 14n + -49 = 0 Reorder the terms: -49 + 14n + 7n2 = 0 Solving -49 + 14n + 7n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '7'. 7(-7 + 2n + n2) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(-7 + 2n + n2)' equal to zero and attempt to solve: Simplifying -7 + 2n + n2 = 0 Solving -7 + 2n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + 2n + 7 + n2 = 0 + 7 Reorder the terms: -7 + 7 + 2n + n2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 2n + n2 = 0 + 7 2n + n2 = 0 + 7 Combine like terms: 0 + 7 = 7 2n + n2 = 7 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 = 7 + 1 Reorder the terms: 1 + 2n + n2 = 7 + 1 Combine like terms: 7 + 1 = 8 1 + 2n + n2 = 8 Factor a perfect square on the left side: (n + 1)(n + 1) = 8 Calculate the square root of the right side: 2.828427125 Break this problem into two subproblems by setting (n + 1) equal to 2.828427125 and -2.828427125.Subproblem 1
n + 1 = 2.828427125 Simplifying n + 1 = 2.828427125 Reorder the terms: 1 + n = 2.828427125 Solving 1 + n = 2.828427125 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 = 2.828427125 + -1 Combine like terms: 1 + -1 = 0 0 + n = 2.828427125 + -1 n = 2.828427125 + -1 Combine like terms: 2.828427125 + -1 = 1.828427125 n = 1.828427125 Simplifying n = 1.828427125Subproblem 2
n + 1 = -2.828427125 Simplifying n + 1 = -2.828427125 Reorder the terms: 1 + n = -2.828427125 Solving 1 + n = -2.828427125 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 = -2.828427125 + -1 Combine like terms: 1 + -1 = 0 0 + n = -2.828427125 + -1 n = -2.828427125 + -1 Combine like terms: -2.828427125 + -1 = -3.828427125 n = -3.828427125 Simplifying n = -3.828427125Solution
The solution to the problem is based on the solutions from the subproblems. n = {1.828427125, -3.828427125}Solution
n = {1.828427125, -3.828427125}
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