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Simplifying 6x2 + -45x + 144 = 0 Reorder the terms: 144 + -45x + 6x2 = 0 Solving 144 + -45x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(48 + -15x + 2x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(48 + -15x + 2x2)' equal to zero and attempt to solve: Simplifying 48 + -15x + 2x2 = 0 Solving 48 + -15x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 24 + -7.5x + x2 = 0 Move the constant term to the right: Add '-24' to each side of the equation. 24 + -7.5x + -24 + x2 = 0 + -24 Reorder the terms: 24 + -24 + -7.5x + x2 = 0 + -24 Combine like terms: 24 + -24 = 0 0 + -7.5x + x2 = 0 + -24 -7.5x + x2 = 0 + -24 Combine like terms: 0 + -24 = -24 -7.5x + x2 = -24 The x term is -7.5x. Take half its coefficient (-3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. -7.5x + 14.0625 + x2 = -24 + 14.0625 Reorder the terms: 14.0625 + -7.5x + x2 = -24 + 14.0625 Combine like terms: -24 + 14.0625 = -9.9375 14.0625 + -7.5x + x2 = -9.9375 Factor a perfect square on the left side: (x + -3.75)(x + -3.75) = -9.9375 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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