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Simplifying 12a2 + 32a + 140 = 0 Reorder the terms: 140 + 32a + 12a2 = 0 Solving 140 + 32a + 12a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '4'. 4(35 + 8a + 3a2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(35 + 8a + 3a2)' equal to zero and attempt to solve: Simplifying 35 + 8a + 3a2 = 0 Solving 35 + 8a + 3a2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 11.66666667 + 2.666666667a + a2 = 0 Move the constant term to the right: Add '-11.66666667' to each side of the equation. 11.66666667 + 2.666666667a + -11.66666667 + a2 = 0 + -11.66666667 Reorder the terms: 11.66666667 + -11.66666667 + 2.666666667a + a2 = 0 + -11.66666667 Combine like terms: 11.66666667 + -11.66666667 = 0.00000000 0.00000000 + 2.666666667a + a2 = 0 + -11.66666667 2.666666667a + a2 = 0 + -11.66666667 Combine like terms: 0 + -11.66666667 = -11.66666667 2.666666667a + a2 = -11.66666667 The a term is 2.666666667a. Take half its coefficient (1.333333334). Square it (1.777777780) and add it to both sides. Add '1.777777780' to each side of the equation. 2.666666667a + 1.777777780 + a2 = -11.66666667 + 1.777777780 Reorder the terms: 1.777777780 + 2.666666667a + a2 = -11.66666667 + 1.777777780 Combine like terms: -11.66666667 + 1.777777780 = -9.88888889 1.777777780 + 2.666666667a + a2 = -9.88888889 Factor a perfect square on the left side: (a + 1.333333334)(a + 1.333333334) = -9.88888889 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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