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Simplifying 2x2 + -6x + 32 = 0 Reorder the terms: 32 + -6x + 2x2 = 0 Solving 32 + -6x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(16 + -3x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(16 + -3x + x2)' equal to zero and attempt to solve: Simplifying 16 + -3x + x2 = 0 Solving 16 + -3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-16' to each side of the equation. 16 + -3x + -16 + x2 = 0 + -16 Reorder the terms: 16 + -16 + -3x + x2 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + -3x + x2 = 0 + -16 -3x + x2 = 0 + -16 Combine like terms: 0 + -16 = -16 -3x + x2 = -16 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 = -16 + 2.25 Reorder the terms: 2.25 + -3x + x2 = -16 + 2.25 Combine like terms: -16 + 2.25 = -13.75 2.25 + -3x + x2 = -13.75 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = -13.75 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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