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Simplifying 2x2 + 6x + 24 = 0 Reorder the terms: 24 + 6x + 2x2 = 0 Solving 24 + 6x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(12 + 3x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(12 + 3x + x2)' equal to zero and attempt to solve: Simplifying 12 + 3x + x2 = 0 Solving 12 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-12' to each side of the equation. 12 + 3x + -12 + x2 = 0 + -12 Reorder the terms: 12 + -12 + 3x + x2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + 3x + x2 = 0 + -12 3x + x2 = 0 + -12 Combine like terms: 0 + -12 = -12 3x + x2 = -12 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 = -12 + 2.25 Reorder the terms: 2.25 + 3x + x2 = -12 + 2.25 Combine like terms: -12 + 2.25 = -9.75 2.25 + 3x + x2 = -9.75 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = -9.75 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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