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Simplifying 0 = x2 + 18x + 120 Reorder the terms: 0 = 120 + 18x + x2 Solving 0 = 120 + 18x + x2 Solving for variable 'x'. Combine like terms: 0 + -120 = -120 -120 + -18x + -1x2 = 120 + 18x + x2 + -120 + -18x + -1x2 Reorder the terms: -120 + -18x + -1x2 = 120 + -120 + 18x + -18x + x2 + -1x2 Combine like terms: 120 + -120 = 0 -120 + -18x + -1x2 = 0 + 18x + -18x + x2 + -1x2 -120 + -18x + -1x2 = 18x + -18x + x2 + -1x2 Combine like terms: 18x + -18x = 0 -120 + -18x + -1x2 = 0 + x2 + -1x2 -120 + -18x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -120 + -18x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(120 + 18x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(120 + 18x + x2)' equal to zero and attempt to solve: Simplifying 120 + 18x + x2 = 0 Solving 120 + 18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-120' to each side of the equation. 120 + 18x + -120 + x2 = 0 + -120 Reorder the terms: 120 + -120 + 18x + x2 = 0 + -120 Combine like terms: 120 + -120 = 0 0 + 18x + x2 = 0 + -120 18x + x2 = 0 + -120 Combine like terms: 0 + -120 = -120 18x + x2 = -120 The x term is 18x. Take half its coefficient (9). Square it (81) and add it to both sides. Add '81' to each side of the equation. 18x + 81 + x2 = -120 + 81 Reorder the terms: 81 + 18x + x2 = -120 + 81 Combine like terms: -120 + 81 = -39 81 + 18x + x2 = -39 Factor a perfect square on the left side: (x + 9)(x + 9) = -39 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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