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Simplifying 8a2 + -10a + 12 = 0 Reorder the terms: 12 + -10a + 8a2 = 0 Solving 12 + -10a + 8a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '2'. 2(6 + -5a + 4a2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(6 + -5a + 4a2)' equal to zero and attempt to solve: Simplifying 6 + -5a + 4a2 = 0 Solving 6 + -5a + 4a2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.5 + -1.25a + a2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + -1.25a + -1.5 + a2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + -1.25a + a2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + -1.25a + a2 = 0 + -1.5 -1.25a + a2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 -1.25a + a2 = -1.5 The a term is -1.25a. 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. -1.25a + 0.390625 + a2 = -1.5 + 0.390625 Reorder the terms: 0.390625 + -1.25a + a2 = -1.5 + 0.390625 Combine like terms: -1.5 + 0.390625 = -1.109375 0.390625 + -1.25a + a2 = -1.109375 Factor a perfect square on the left side: (a + -0.625)(a + -0.625) = -1.109375 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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