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Simplifying 0 = x2 + 12x + 38 Reorder the terms: 0 = 38 + 12x + x2 Solving 0 = 38 + 12x + x2 Solving for variable 'x'. Combine like terms: 0 + -38 = -38 -38 + -12x + -1x2 = 38 + 12x + x2 + -38 + -12x + -1x2 Reorder the terms: -38 + -12x + -1x2 = 38 + -38 + 12x + -12x + x2 + -1x2 Combine like terms: 38 + -38 = 0 -38 + -12x + -1x2 = 0 + 12x + -12x + x2 + -1x2 -38 + -12x + -1x2 = 12x + -12x + x2 + -1x2 Combine like terms: 12x + -12x = 0 -38 + -12x + -1x2 = 0 + x2 + -1x2 -38 + -12x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -38 + -12x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(38 + 12x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(38 + 12x + x2)' equal to zero and attempt to solve: Simplifying 38 + 12x + x2 = 0 Solving 38 + 12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-38' to each side of the equation. 38 + 12x + -38 + x2 = 0 + -38 Reorder the terms: 38 + -38 + 12x + x2 = 0 + -38 Combine like terms: 38 + -38 = 0 0 + 12x + x2 = 0 + -38 12x + x2 = 0 + -38 Combine like terms: 0 + -38 = -38 12x + x2 = -38 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 = -38 + 36 Reorder the terms: 36 + 12x + x2 = -38 + 36 Combine like terms: -38 + 36 = -2 36 + 12x + x2 = -2 Factor a perfect square on the left side: (x + 6)(x + 6) = -2 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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