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Simplifying 0 = x2 + 12x + 37 Reorder the terms: 0 = 37 + 12x + x2 Solving 0 = 37 + 12x + x2 Solving for variable 'x'. Combine like terms: 0 + -37 = -37 -37 + -12x + -1x2 = 37 + 12x + x2 + -37 + -12x + -1x2 Reorder the terms: -37 + -12x + -1x2 = 37 + -37 + 12x + -12x + x2 + -1x2 Combine like terms: 37 + -37 = 0 -37 + -12x + -1x2 = 0 + 12x + -12x + x2 + -1x2 -37 + -12x + -1x2 = 12x + -12x + x2 + -1x2 Combine like terms: 12x + -12x = 0 -37 + -12x + -1x2 = 0 + x2 + -1x2 -37 + -12x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -37 + -12x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(37 + 12x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(37 + 12x + x2)' equal to zero and attempt to solve: Simplifying 37 + 12x + x2 = 0 Solving 37 + 12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-37' to each side of the equation. 37 + 12x + -37 + x2 = 0 + -37 Reorder the terms: 37 + -37 + 12x + x2 = 0 + -37 Combine like terms: 37 + -37 = 0 0 + 12x + x2 = 0 + -37 12x + x2 = 0 + -37 Combine like terms: 0 + -37 = -37 12x + x2 = -37 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 = -37 + 36 Reorder the terms: 36 + 12x + x2 = -37 + 36 Combine like terms: -37 + 36 = -1 36 + 12x + x2 = -1 Factor a perfect square on the left side: (x + 6)(x + 6) = -1 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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