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Simplifying 2n2 + 10n + -42 = 0 Reorder the terms: -42 + 10n + 2n2 = 0 Solving -42 + 10n + 2n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '2'. 2(-21 + 5n + n2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-21 + 5n + n2)' equal to zero and attempt to solve: Simplifying -21 + 5n + n2 = 0 Solving -21 + 5n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '21' to each side of the equation. -21 + 5n + 21 + n2 = 0 + 21 Reorder the terms: -21 + 21 + 5n + n2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + 5n + n2 = 0 + 21 5n + n2 = 0 + 21 Combine like terms: 0 + 21 = 21 5n + n2 = 21 The n term is 5n. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5n + 6.25 + n2 = 21 + 6.25 Reorder the terms: 6.25 + 5n + n2 = 21 + 6.25 Combine like terms: 21 + 6.25 = 27.25 6.25 + 5n + n2 = 27.25 Factor a perfect square on the left side: (n + 2.5)(n + 2.5) = 27.25 Calculate the square root of the right side: 5.220153254 Break this problem into two subproblems by setting (n + 2.5) equal to 5.220153254 and -5.220153254.Subproblem 1
n + 2.5 = 5.220153254 Simplifying n + 2.5 = 5.220153254 Reorder the terms: 2.5 + n = 5.220153254 Solving 2.5 + n = 5.220153254 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + n = 5.220153254 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + n = 5.220153254 + -2.5 n = 5.220153254 + -2.5 Combine like terms: 5.220153254 + -2.5 = 2.720153254 n = 2.720153254 Simplifying n = 2.720153254Subproblem 2
n + 2.5 = -5.220153254 Simplifying n + 2.5 = -5.220153254 Reorder the terms: 2.5 + n = -5.220153254 Solving 2.5 + n = -5.220153254 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + n = -5.220153254 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + n = -5.220153254 + -2.5 n = -5.220153254 + -2.5 Combine like terms: -5.220153254 + -2.5 = -7.720153254 n = -7.720153254 Simplifying n = -7.720153254Solution
The solution to the problem is based on the solutions from the subproblems. n = {2.720153254, -7.720153254}Solution
n = {2.720153254, -7.720153254}
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