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Simplifying -15a2 = 13a + 20 Reorder the terms: -15a2 = 20 + 13a Solving -15a2 = 20 + 13a Solving for variable 'a'. Reorder the terms: -20 + -13a + -15a2 = 20 + 13a + -20 + -13a Reorder the terms: -20 + -13a + -15a2 = 20 + -20 + 13a + -13a Combine like terms: 20 + -20 = 0 -20 + -13a + -15a2 = 0 + 13a + -13a -20 + -13a + -15a2 = 13a + -13a Combine like terms: 13a + -13a = 0 -20 + -13a + -15a2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(20 + 13a + 15a2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(20 + 13a + 15a2)' equal to zero and attempt to solve: Simplifying 20 + 13a + 15a2 = 0 Solving 20 + 13a + 15a2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. 1.333333333 + 0.8666666667a + a2 = 0 Move the constant term to the right: Add '-1.333333333' to each side of the equation. 1.333333333 + 0.8666666667a + -1.333333333 + a2 = 0 + -1.333333333 Reorder the terms: 1.333333333 + -1.333333333 + 0.8666666667a + a2 = 0 + -1.333333333 Combine like terms: 1.333333333 + -1.333333333 = 0.000000000 0.000000000 + 0.8666666667a + a2 = 0 + -1.333333333 0.8666666667a + a2 = 0 + -1.333333333 Combine like terms: 0 + -1.333333333 = -1.333333333 0.8666666667a + a2 = -1.333333333 The a term is 0.8666666667a. Take half its coefficient (0.4333333334). Square it (0.1877777778) and add it to both sides. Add '0.1877777778' to each side of the equation. 0.8666666667a + 0.1877777778 + a2 = -1.333333333 + 0.1877777778 Reorder the terms: 0.1877777778 + 0.8666666667a + a2 = -1.333333333 + 0.1877777778 Combine like terms: -1.333333333 + 0.1877777778 = -1.1455555552 0.1877777778 + 0.8666666667a + a2 = -1.1455555552 Factor a perfect square on the left side: (a + 0.4333333334)(a + 0.4333333334) = -1.1455555552 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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