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Simplifying 216 = 24x + -2x2 Solving 216 = 24x + -2x2 Solving for variable 'x'. Reorder the terms: 216 + -24x + 2x2 = 24x + -24x + -2x2 + 2x2 Combine like terms: 24x + -24x = 0 216 + -24x + 2x2 = 0 + -2x2 + 2x2 216 + -24x + 2x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 216 + -24x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(108 + -12x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(108 + -12x + x2)' equal to zero and attempt to solve: Simplifying 108 + -12x + x2 = 0 Solving 108 + -12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-108' to each side of the equation. 108 + -12x + -108 + x2 = 0 + -108 Reorder the terms: 108 + -108 + -12x + x2 = 0 + -108 Combine like terms: 108 + -108 = 0 0 + -12x + x2 = 0 + -108 -12x + x2 = 0 + -108 Combine like terms: 0 + -108 = -108 -12x + x2 = -108 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = -108 + 36 Reorder the terms: 36 + -12x + x2 = -108 + 36 Combine like terms: -108 + 36 = -72 36 + -12x + x2 = -72 Factor a perfect square on the left side: (x + -6)(x + -6) = -72 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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