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Simplifying -9n2 = 4 + 7n Solving -9n2 = 4 + 7n Solving for variable 'n'. Reorder the terms: -4 + -7n + -9n2 = 4 + 7n + -4 + -7n Reorder the terms: -4 + -7n + -9n2 = 4 + -4 + 7n + -7n Combine like terms: 4 + -4 = 0 -4 + -7n + -9n2 = 0 + 7n + -7n -4 + -7n + -9n2 = 7n + -7n Combine like terms: 7n + -7n = 0 -4 + -7n + -9n2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(4 + 7n + 9n2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(4 + 7n + 9n2)' equal to zero and attempt to solve: Simplifying 4 + 7n + 9n2 = 0 Solving 4 + 7n + 9n2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.4444444444 + 0.7777777778n + n2 = 0 Move the constant term to the right: Add '-0.4444444444' to each side of the equation. 0.4444444444 + 0.7777777778n + -0.4444444444 + n2 = 0 + -0.4444444444 Reorder the terms: 0.4444444444 + -0.4444444444 + 0.7777777778n + n2 = 0 + -0.4444444444 Combine like terms: 0.4444444444 + -0.4444444444 = 0.0000000000 0.0000000000 + 0.7777777778n + n2 = 0 + -0.4444444444 0.7777777778n + n2 = 0 + -0.4444444444 Combine like terms: 0 + -0.4444444444 = -0.4444444444 0.7777777778n + n2 = -0.4444444444 The n term is 0.7777777778n. Take half its coefficient (0.3888888889). Square it (0.1512345679) and add it to both sides. Add '0.1512345679' to each side of the equation. 0.7777777778n + 0.1512345679 + n2 = -0.4444444444 + 0.1512345679 Reorder the terms: 0.1512345679 + 0.7777777778n + n2 = -0.4444444444 + 0.1512345679 Combine like terms: -0.4444444444 + 0.1512345679 = -0.2932098765 0.1512345679 + 0.7777777778n + n2 = -0.2932098765 Factor a perfect square on the left side: (n + 0.3888888889)(n + 0.3888888889) = -0.2932098765 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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