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Simplifying 0 = x2 + 4x + 60 Reorder the terms: 0 = 60 + 4x + x2 Solving 0 = 60 + 4x + x2 Solving for variable 'x'. Combine like terms: 0 + -60 = -60 -60 + -4x + -1x2 = 60 + 4x + x2 + -60 + -4x + -1x2 Reorder the terms: -60 + -4x + -1x2 = 60 + -60 + 4x + -4x + x2 + -1x2 Combine like terms: 60 + -60 = 0 -60 + -4x + -1x2 = 0 + 4x + -4x + x2 + -1x2 -60 + -4x + -1x2 = 4x + -4x + x2 + -1x2 Combine like terms: 4x + -4x = 0 -60 + -4x + -1x2 = 0 + x2 + -1x2 -60 + -4x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -60 + -4x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(60 + 4x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(60 + 4x + x2)' equal to zero and attempt to solve: Simplifying 60 + 4x + x2 = 0 Solving 60 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-60' to each side of the equation. 60 + 4x + -60 + x2 = 0 + -60 Reorder the terms: 60 + -60 + 4x + x2 = 0 + -60 Combine like terms: 60 + -60 = 0 0 + 4x + x2 = 0 + -60 4x + x2 = 0 + -60 Combine like terms: 0 + -60 = -60 4x + x2 = -60 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = -60 + 4 Reorder the terms: 4 + 4x + x2 = -60 + 4 Combine like terms: -60 + 4 = -56 4 + 4x + x2 = -56 Factor a perfect square on the left side: (x + 2)(x + 2) = -56 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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