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Simplifying 12a2 + -21a + 189 = 0 Reorder the terms: 189 + -21a + 12a2 = 0 Solving 189 + -21a + 12a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '3'. 3(63 + -7a + 4a2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(63 + -7a + 4a2)' equal to zero and attempt to solve: Simplifying 63 + -7a + 4a2 = 0 Solving 63 + -7a + 4a2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 15.75 + -1.75a + a2 = 0 Move the constant term to the right: Add '-15.75' to each side of the equation. 15.75 + -1.75a + -15.75 + a2 = 0 + -15.75 Reorder the terms: 15.75 + -15.75 + -1.75a + a2 = 0 + -15.75 Combine like terms: 15.75 + -15.75 = 0.00 0.00 + -1.75a + a2 = 0 + -15.75 -1.75a + a2 = 0 + -15.75 Combine like terms: 0 + -15.75 = -15.75 -1.75a + a2 = -15.75 The a term is -1.75a. Take half its coefficient (-0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. -1.75a + 0.765625 + a2 = -15.75 + 0.765625 Reorder the terms: 0.765625 + -1.75a + a2 = -15.75 + 0.765625 Combine like terms: -15.75 + 0.765625 = -14.984375 0.765625 + -1.75a + a2 = -14.984375 Factor a perfect square on the left side: (a + -0.875)(a + -0.875) = -14.984375 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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