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Simplifying 0 = 3x2 + 9x + 540 Reorder the terms: 0 = 540 + 9x + 3x2 Solving 0 = 540 + 9x + 3x2 Solving for variable 'x'. Combine like terms: 0 + -540 = -540 -540 + -9x + -3x2 = 540 + 9x + 3x2 + -540 + -9x + -3x2 Reorder the terms: -540 + -9x + -3x2 = 540 + -540 + 9x + -9x + 3x2 + -3x2 Combine like terms: 540 + -540 = 0 -540 + -9x + -3x2 = 0 + 9x + -9x + 3x2 + -3x2 -540 + -9x + -3x2 = 9x + -9x + 3x2 + -3x2 Combine like terms: 9x + -9x = 0 -540 + -9x + -3x2 = 0 + 3x2 + -3x2 -540 + -9x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -540 + -9x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '-3'. -3(180 + 3x + x2) = 0 Ignore the factor -3.Subproblem 1
Set the factor '(180 + 3x + x2)' equal to zero and attempt to solve: Simplifying 180 + 3x + x2 = 0 Solving 180 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-180' to each side of the equation. 180 + 3x + -180 + x2 = 0 + -180 Reorder the terms: 180 + -180 + 3x + x2 = 0 + -180 Combine like terms: 180 + -180 = 0 0 + 3x + x2 = 0 + -180 3x + x2 = 0 + -180 Combine like terms: 0 + -180 = -180 3x + x2 = -180 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = -180 + 2.25 Reorder the terms: 2.25 + 3x + x2 = -180 + 2.25 Combine like terms: -180 + 2.25 = -177.75 2.25 + 3x + x2 = -177.75 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = -177.75 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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