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Simplifying 12x2 + -78x + 360 = 0 Reorder the terms: 360 + -78x + 12x2 = 0 Solving 360 + -78x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(60 + -13x + 2x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(60 + -13x + 2x2)' equal to zero and attempt to solve: Simplifying 60 + -13x + 2x2 = 0 Solving 60 + -13x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 30 + -6.5x + x2 = 0 Move the constant term to the right: Add '-30' to each side of the equation. 30 + -6.5x + -30 + x2 = 0 + -30 Reorder the terms: 30 + -30 + -6.5x + x2 = 0 + -30 Combine like terms: 30 + -30 = 0 0 + -6.5x + x2 = 0 + -30 -6.5x + x2 = 0 + -30 Combine like terms: 0 + -30 = -30 -6.5x + x2 = -30 The x term is -6.5x. Take half its coefficient (-3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. -6.5x + 10.5625 + x2 = -30 + 10.5625 Reorder the terms: 10.5625 + -6.5x + x2 = -30 + 10.5625 Combine like terms: -30 + 10.5625 = -19.4375 10.5625 + -6.5x + x2 = -19.4375 Factor a perfect square on the left side: (x + -3.25)(x + -3.25) = -19.4375 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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