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Simplifying -11 + -5a = 6a(5a + 4) Reorder the terms: -11 + -5a = 6a(4 + 5a) -11 + -5a = (4 * 6a + 5a * 6a) -11 + -5a = (24a + 30a2) Solving -11 + -5a = 24a + 30a2 Solving for variable 'a'. Combine like terms: -5a + -24a = -29a -11 + -29a + -30a2 = 24a + 30a2 + -24a + -30a2 Reorder the terms: -11 + -29a + -30a2 = 24a + -24a + 30a2 + -30a2 Combine like terms: 24a + -24a = 0 -11 + -29a + -30a2 = 0 + 30a2 + -30a2 -11 + -29a + -30a2 = 30a2 + -30a2 Combine like terms: 30a2 + -30a2 = 0 -11 + -29a + -30a2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(11 + 29a + 30a2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(11 + 29a + 30a2)' equal to zero and attempt to solve: Simplifying 11 + 29a + 30a2 = 0 Solving 11 + 29a + 30a2 = 0 Begin completing the square. Divide all terms by 30 the coefficient of the squared term: Divide each side by '30'. 0.3666666667 + 0.9666666667a + a2 = 0.0 Move the constant term to the right: Add '-0.3666666667' to each side of the equation. 0.3666666667 + 0.9666666667a + -0.3666666667 + a2 = 0.0 + -0.3666666667 Reorder the terms: 0.3666666667 + -0.3666666667 + 0.9666666667a + a2 = 0.0 + -0.3666666667 Combine like terms: 0.3666666667 + -0.3666666667 = 0.0000000000 0.0000000000 + 0.9666666667a + a2 = 0.0 + -0.3666666667 0.9666666667a + a2 = 0.0 + -0.3666666667 Combine like terms: 0.0 + -0.3666666667 = -0.3666666667 0.9666666667a + a2 = -0.3666666667 The a term is 0.9666666667a. Take half its coefficient (0.4833333334). Square it (0.2336111112) and add it to both sides. Add '0.2336111112' to each side of the equation. 0.9666666667a + 0.2336111112 + a2 = -0.3666666667 + 0.2336111112 Reorder the terms: 0.2336111112 + 0.9666666667a + a2 = -0.3666666667 + 0.2336111112 Combine like terms: -0.3666666667 + 0.2336111112 = -0.1330555555 0.2336111112 + 0.9666666667a + a2 = -0.1330555555 Factor a perfect square on the left side: (a + 0.4833333334)(a + 0.4833333334) = -0.1330555555 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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