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Simplifying 12x2 + -6x + 15 = 0 Reorder the terms: 15 + -6x + 12x2 = 0 Solving 15 + -6x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(5 + -2x + 4x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(5 + -2x + 4x2)' equal to zero and attempt to solve: Simplifying 5 + -2x + 4x2 = 0 Solving 5 + -2x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.25 + -0.5x + x2 = 0 Move the constant term to the right: Add '-1.25' to each side of the equation. 1.25 + -0.5x + -1.25 + x2 = 0 + -1.25 Reorder the terms: 1.25 + -1.25 + -0.5x + x2 = 0 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + -0.5x + x2 = 0 + -1.25 -0.5x + x2 = 0 + -1.25 Combine like terms: 0 + -1.25 = -1.25 -0.5x + x2 = -1.25 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = -1.25 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = -1.25 + 0.0625 Combine like terms: -1.25 + 0.0625 = -1.1875 0.0625 + -0.5x + x2 = -1.1875 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = -1.1875 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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