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Simplifying 0 = 2n2 + 29n + 636 Reorder the terms: 0 = 636 + 29n + 2n2 Solving 0 = 636 + 29n + 2n2 Solving for variable 'n'. Combine like terms: 0 + -636 = -636 -636 + -29n + -2n2 = 636 + 29n + 2n2 + -636 + -29n + -2n2 Reorder the terms: -636 + -29n + -2n2 = 636 + -636 + 29n + -29n + 2n2 + -2n2 Combine like terms: 636 + -636 = 0 -636 + -29n + -2n2 = 0 + 29n + -29n + 2n2 + -2n2 -636 + -29n + -2n2 = 29n + -29n + 2n2 + -2n2 Combine like terms: 29n + -29n = 0 -636 + -29n + -2n2 = 0 + 2n2 + -2n2 -636 + -29n + -2n2 = 2n2 + -2n2 Combine like terms: 2n2 + -2n2 = 0 -636 + -29n + -2n2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(636 + 29n + 2n2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(636 + 29n + 2n2)' equal to zero and attempt to solve: Simplifying 636 + 29n + 2n2 = 0 Solving 636 + 29n + 2n2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 318 + 14.5n + n2 = 0 Move the constant term to the right: Add '-318' to each side of the equation. 318 + 14.5n + -318 + n2 = 0 + -318 Reorder the terms: 318 + -318 + 14.5n + n2 = 0 + -318 Combine like terms: 318 + -318 = 0 0 + 14.5n + n2 = 0 + -318 14.5n + n2 = 0 + -318 Combine like terms: 0 + -318 = -318 14.5n + n2 = -318 The n term is 14.5n. Take half its coefficient (7.25). Square it (52.5625) and add it to both sides. Add '52.5625' to each side of the equation. 14.5n + 52.5625 + n2 = -318 + 52.5625 Reorder the terms: 52.5625 + 14.5n + n2 = -318 + 52.5625 Combine like terms: -318 + 52.5625 = -265.4375 52.5625 + 14.5n + n2 = -265.4375 Factor a perfect square on the left side: (n + 7.25)(n + 7.25) = -265.4375 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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