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Simplifying 120x2 + -78x + 120 = 0 Reorder the terms: 120 + -78x + 120x2 = 0 Solving 120 + -78x + 120x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(20 + -13x + 20x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(20 + -13x + 20x2)' equal to zero and attempt to solve: Simplifying 20 + -13x + 20x2 = 0 Solving 20 + -13x + 20x2 = 0 Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. 1 + -0.65x + x2 = 0.0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -0.65x + -1 + x2 = 0.0 + -1 Reorder the terms: 1 + -1 + -0.65x + x2 = 0.0 + -1 Combine like terms: 1 + -1 = 0 0 + -0.65x + x2 = 0.0 + -1 -0.65x + x2 = 0.0 + -1 Combine like terms: 0.0 + -1 = -1 -0.65x + x2 = -1 The x term is -0.65x. Take half its coefficient (-0.325). Square it (0.105625) and add it to both sides. Add '0.105625' to each side of the equation. -0.65x + 0.105625 + x2 = -1 + 0.105625 Reorder the terms: 0.105625 + -0.65x + x2 = -1 + 0.105625 Combine like terms: -1 + 0.105625 = -0.894375 0.105625 + -0.65x + x2 = -0.894375 Factor a perfect square on the left side: (x + -0.325)(x + -0.325) = -0.894375 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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