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Simplifying (2x2) + (26x) + (156) = 0 (2x2) + (26x) + 156 = 0 Reorder the terms: 156 + (26x) + (2x2) = 0 Solving 156 + (26x) + (2x2) = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(78 + (13x) + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(78 + (13x) + x2)' equal to zero and attempt to solve: Simplifying 78 + (13x) + x2 = 0 Solving 78 + (13x) + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-78' to each side of the equation. 78 + (13x) + -78 + x2 = 0 + -78 Reorder the terms: 78 + -78 + (13x) + x2 = 0 + -78 Combine like terms: 78 + -78 = 0 0 + (13x) + x2 = 0 + -78 (13x) + x2 = 0 + -78 Combine like terms: 0 + -78 = -78 (13x) + x2 = -78 The x term is (13x). Take half its coefficient (6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. (13x) + 42.25 + x2 = -78 + 42.25 Reorder the terms: 42.25 + (13x) + x2 = -78 + 42.25 Combine like terms: -78 + 42.25 = -35.75 42.25 + (13x) + x2 = -35.75 Factor a perfect square on the left side: (x + 6.5)(x + 6.5) = -35.75 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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