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Simplifying 33 = -3x2 + 6x + 12 Reorder the terms: 33 = 12 + 6x + -3x2 Solving 33 = 12 + 6x + -3x2 Solving for variable 'x'. Combine like terms: 33 + -12 = 21 21 + -6x + 3x2 = 12 + 6x + -3x2 + -12 + -6x + 3x2 Reorder the terms: 21 + -6x + 3x2 = 12 + -12 + 6x + -6x + -3x2 + 3x2 Combine like terms: 12 + -12 = 0 21 + -6x + 3x2 = 0 + 6x + -6x + -3x2 + 3x2 21 + -6x + 3x2 = 6x + -6x + -3x2 + 3x2 Combine like terms: 6x + -6x = 0 21 + -6x + 3x2 = 0 + -3x2 + 3x2 21 + -6x + 3x2 = -3x2 + 3x2 Combine like terms: -3x2 + 3x2 = 0 21 + -6x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(7 + -2x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(7 + -2x + x2)' equal to zero and attempt to solve: Simplifying 7 + -2x + x2 = 0 Solving 7 + -2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-7' to each side of the equation. 7 + -2x + -7 + x2 = 0 + -7 Reorder the terms: 7 + -7 + -2x + x2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -2x + x2 = 0 + -7 -2x + x2 = 0 + -7 Combine like terms: 0 + -7 = -7 -2x + x2 = -7 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = -7 + 1 Reorder the terms: 1 + -2x + x2 = -7 + 1 Combine like terms: -7 + 1 = -6 1 + -2x + x2 = -6 Factor a perfect square on the left side: (x + -1)(x + -1) = -6 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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