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Simplifying 42n2 + -3n + -42 = 0 Reorder the terms: -42 + -3n + 42n2 = 0 Solving -42 + -3n + 42n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '3'. 3(-14 + -1n + 14n2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-14 + -1n + 14n2)' equal to zero and attempt to solve: Simplifying -14 + -1n + 14n2 = 0 Solving -14 + -1n + 14n2 = 0 Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. -1 + -0.07142857143n + n2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -0.07142857143n + 1 + n2 = 0 + 1 Reorder the terms: -1 + 1 + -0.07142857143n + n2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -0.07142857143n + n2 = 0 + 1 -0.07142857143n + n2 = 0 + 1 Combine like terms: 0 + 1 = 1 -0.07142857143n + n2 = 1 The n term is -0.07142857143n. Take half its coefficient (-0.03571428572). Square it (0.001275510204) and add it to both sides. Add '0.001275510204' to each side of the equation. -0.07142857143n + 0.001275510204 + n2 = 1 + 0.001275510204 Reorder the terms: 0.001275510204 + -0.07142857143n + n2 = 1 + 0.001275510204 Combine like terms: 1 + 0.001275510204 = 1.001275510204 0.001275510204 + -0.07142857143n + n2 = 1.001275510204 Factor a perfect square on the left side: (n + -0.03571428572)(n + -0.03571428572) = 1.001275510204 Calculate the square root of the right side: 1.000637552 Break this problem into two subproblems by setting (n + -0.03571428572) equal to 1.000637552 and -1.000637552.Subproblem 1
n + -0.03571428572 = 1.000637552 Simplifying n + -0.03571428572 = 1.000637552 Reorder the terms: -0.03571428572 + n = 1.000637552 Solving -0.03571428572 + n = 1.000637552 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.03571428572' to each side of the equation. -0.03571428572 + 0.03571428572 + n = 1.000637552 + 0.03571428572 Combine like terms: -0.03571428572 + 0.03571428572 = 0.00000000000 0.00000000000 + n = 1.000637552 + 0.03571428572 n = 1.000637552 + 0.03571428572 Combine like terms: 1.000637552 + 0.03571428572 = 1.03635183772 n = 1.03635183772 Simplifying n = 1.03635183772Subproblem 2
n + -0.03571428572 = -1.000637552 Simplifying n + -0.03571428572 = -1.000637552 Reorder the terms: -0.03571428572 + n = -1.000637552 Solving -0.03571428572 + n = -1.000637552 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.03571428572' to each side of the equation. -0.03571428572 + 0.03571428572 + n = -1.000637552 + 0.03571428572 Combine like terms: -0.03571428572 + 0.03571428572 = 0.00000000000 0.00000000000 + n = -1.000637552 + 0.03571428572 n = -1.000637552 + 0.03571428572 Combine like terms: -1.000637552 + 0.03571428572 = -0.96492326628 n = -0.96492326628 Simplifying n = -0.96492326628Solution
The solution to the problem is based on the solutions from the subproblems. n = {1.03635183772, -0.96492326628}Solution
n = {1.03635183772, -0.96492326628}
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