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Simplifying (3x2) + (42x) + 180 = 0 Reorder the terms: 180 + (42x) + (3x2) = 0 Solving 180 + (42x) + (3x2) = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(60 + (14x) + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(60 + (14x) + x2)' equal to zero and attempt to solve: Simplifying 60 + (14x) + x2 = 0 Solving 60 + (14x) + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-60' to each side of the equation. 60 + (14x) + -60 + x2 = 0 + -60 Reorder the terms: 60 + -60 + (14x) + x2 = 0 + -60 Combine like terms: 60 + -60 = 0 0 + (14x) + x2 = 0 + -60 (14x) + x2 = 0 + -60 Combine like terms: 0 + -60 = -60 (14x) + x2 = -60 The x term is (14x). Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. (14x) + 49 + x2 = -60 + 49 Reorder the terms: 49 + (14x) + x2 = -60 + 49 Combine like terms: -60 + 49 = -11 49 + (14x) + x2 = -11 Factor a perfect square on the left side: (x + 7)(x + 7) = -11 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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