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Simplifying x = x2 + 12x + 36 Reorder the terms: x = 36 + 12x + x2 Solving x = 36 + 12x + x2 Solving for variable 'x'. Reorder the terms: -36 + x + -12x + -1x2 = 36 + 12x + x2 + -36 + -12x + -1x2 Combine like terms: x + -12x = -11x -36 + -11x + -1x2 = 36 + 12x + x2 + -36 + -12x + -1x2 Reorder the terms: -36 + -11x + -1x2 = 36 + -36 + 12x + -12x + x2 + -1x2 Combine like terms: 36 + -36 = 0 -36 + -11x + -1x2 = 0 + 12x + -12x + x2 + -1x2 -36 + -11x + -1x2 = 12x + -12x + x2 + -1x2 Combine like terms: 12x + -12x = 0 -36 + -11x + -1x2 = 0 + x2 + -1x2 -36 + -11x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -36 + -11x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(36 + 11x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(36 + 11x + x2)' equal to zero and attempt to solve: Simplifying 36 + 11x + x2 = 0 Solving 36 + 11x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-36' to each side of the equation. 36 + 11x + -36 + x2 = 0 + -36 Reorder the terms: 36 + -36 + 11x + x2 = 0 + -36 Combine like terms: 36 + -36 = 0 0 + 11x + x2 = 0 + -36 11x + x2 = 0 + -36 Combine like terms: 0 + -36 = -36 11x + x2 = -36 The x term is 11x. Take half its coefficient (5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. 11x + 30.25 + x2 = -36 + 30.25 Reorder the terms: 30.25 + 11x + x2 = -36 + 30.25 Combine like terms: -36 + 30.25 = -5.75 30.25 + 11x + x2 = -5.75 Factor a perfect square on the left side: (x + 5.5)(x + 5.5) = -5.75 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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