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Simplifying 12x2 + -15x + 42 = 0 Reorder the terms: 42 + -15x + 12x2 = 0 Solving 42 + -15x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(14 + -5x + 4x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(14 + -5x + 4x2)' equal to zero and attempt to solve: Simplifying 14 + -5x + 4x2 = 0 Solving 14 + -5x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 3.5 + -1.25x + x2 = 0 Move the constant term to the right: Add '-3.5' to each side of the equation. 3.5 + -1.25x + -3.5 + x2 = 0 + -3.5 Reorder the terms: 3.5 + -3.5 + -1.25x + x2 = 0 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + -1.25x + x2 = 0 + -3.5 -1.25x + x2 = 0 + -3.5 Combine like terms: 0 + -3.5 = -3.5 -1.25x + x2 = -3.5 The x term is -1.25x. Take half its coefficient (-0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. -1.25x + 0.390625 + x2 = -3.5 + 0.390625 Reorder the terms: 0.390625 + -1.25x + x2 = -3.5 + 0.390625 Combine like terms: -3.5 + 0.390625 = -3.109375 0.390625 + -1.25x + x2 = -3.109375 Factor a perfect square on the left side: (x + -0.625)(x + -0.625) = -3.109375 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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