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Simplifying 0 = 12x2 + -16x + 88 Reorder the terms: 0 = 88 + -16x + 12x2 Solving 0 = 88 + -16x + 12x2 Solving for variable 'x'. Combine like terms: 0 + -88 = -88 -88 + 16x + -12x2 = 88 + -16x + 12x2 + -88 + 16x + -12x2 Reorder the terms: -88 + 16x + -12x2 = 88 + -88 + -16x + 16x + 12x2 + -12x2 Combine like terms: 88 + -88 = 0 -88 + 16x + -12x2 = 0 + -16x + 16x + 12x2 + -12x2 -88 + 16x + -12x2 = -16x + 16x + 12x2 + -12x2 Combine like terms: -16x + 16x = 0 -88 + 16x + -12x2 = 0 + 12x2 + -12x2 -88 + 16x + -12x2 = 12x2 + -12x2 Combine like terms: 12x2 + -12x2 = 0 -88 + 16x + -12x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-22 + 4x + -3x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-22 + 4x + -3x2)' equal to zero and attempt to solve: Simplifying -22 + 4x + -3x2 = 0 Solving -22 + 4x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 7.333333333 + -1.333333333x + x2 = 0 Move the constant term to the right: Add '-7.333333333' to each side of the equation. 7.333333333 + -1.333333333x + -7.333333333 + x2 = 0 + -7.333333333 Reorder the terms: 7.333333333 + -7.333333333 + -1.333333333x + x2 = 0 + -7.333333333 Combine like terms: 7.333333333 + -7.333333333 = 0.000000000 0.000000000 + -1.333333333x + x2 = 0 + -7.333333333 -1.333333333x + x2 = 0 + -7.333333333 Combine like terms: 0 + -7.333333333 = -7.333333333 -1.333333333x + x2 = -7.333333333 The x term is -1.333333333x. Take half its coefficient (-0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. -1.333333333x + 0.4444444442 + x2 = -7.333333333 + 0.4444444442 Reorder the terms: 0.4444444442 + -1.333333333x + x2 = -7.333333333 + 0.4444444442 Combine like terms: -7.333333333 + 0.4444444442 = -6.8888888888 0.4444444442 + -1.333333333x + x2 = -6.8888888888 Factor a perfect square on the left side: (x + -0.6666666665)(x + -0.6666666665) = -6.8888888888 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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