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Simplifying 3x + 12 + -5x = -24 + -2x2 Reorder the terms: 12 + 3x + -5x = -24 + -2x2 Combine like terms: 3x + -5x = -2x 12 + -2x = -24 + -2x2 Solving 12 + -2x = -24 + -2x2 Solving for variable 'x'. Reorder the terms: 12 + 24 + -2x + 2x2 = -24 + -2x2 + 24 + 2x2 Combine like terms: 12 + 24 = 36 36 + -2x + 2x2 = -24 + -2x2 + 24 + 2x2 Reorder the terms: 36 + -2x + 2x2 = -24 + 24 + -2x2 + 2x2 Combine like terms: -24 + 24 = 0 36 + -2x + 2x2 = 0 + -2x2 + 2x2 36 + -2x + 2x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 36 + -2x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(18 + -1x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(18 + -1x + x2)' equal to zero and attempt to solve: Simplifying 18 + -1x + x2 = 0 Solving 18 + -1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-18' to each side of the equation. 18 + -1x + -18 + x2 = 0 + -18 Reorder the terms: 18 + -18 + -1x + x2 = 0 + -18 Combine like terms: 18 + -18 = 0 0 + -1x + x2 = 0 + -18 -1x + x2 = 0 + -18 Combine like terms: 0 + -18 = -18 -1x + x2 = -18 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = -18 + 0.25 Reorder the terms: 0.25 + -1x + x2 = -18 + 0.25 Combine like terms: -18 + 0.25 = -17.75 0.25 + -1x + x2 = -17.75 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = -17.75 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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