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Simplifying 0 = x2 + 24x + 180 Reorder the terms: 0 = 180 + 24x + x2 Solving 0 = 180 + 24x + x2 Solving for variable 'x'. Combine like terms: 0 + -180 = -180 -180 + -24x + -1x2 = 180 + 24x + x2 + -180 + -24x + -1x2 Reorder the terms: -180 + -24x + -1x2 = 180 + -180 + 24x + -24x + x2 + -1x2 Combine like terms: 180 + -180 = 0 -180 + -24x + -1x2 = 0 + 24x + -24x + x2 + -1x2 -180 + -24x + -1x2 = 24x + -24x + x2 + -1x2 Combine like terms: 24x + -24x = 0 -180 + -24x + -1x2 = 0 + x2 + -1x2 -180 + -24x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -180 + -24x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(180 + 24x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(180 + 24x + x2)' equal to zero and attempt to solve: Simplifying 180 + 24x + x2 = 0 Solving 180 + 24x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-180' to each side of the equation. 180 + 24x + -180 + x2 = 0 + -180 Reorder the terms: 180 + -180 + 24x + x2 = 0 + -180 Combine like terms: 180 + -180 = 0 0 + 24x + x2 = 0 + -180 24x + x2 = 0 + -180 Combine like terms: 0 + -180 = -180 24x + x2 = -180 The x term is 24x. Take half its coefficient (12). Square it (144) and add it to both sides. Add '144' to each side of the equation. 24x + 144 + x2 = -180 + 144 Reorder the terms: 144 + 24x + x2 = -180 + 144 Combine like terms: -180 + 144 = -36 144 + 24x + x2 = -36 Factor a perfect square on the left side: (x + 12)(x + 12) = -36 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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