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Simplifying 8a + -3a(2a + 5) = 13 Reorder the terms: 8a + -3a(5 + 2a) = 13 8a + (5 * -3a + 2a * -3a) = 13 8a + (-15a + -6a2) = 13 Combine like terms: 8a + -15a = -7a -7a + -6a2 = 13 Solving -7a + -6a2 = 13 Solving for variable 'a'. Reorder the terms: -13 + -7a + -6a2 = 13 + -13 Combine like terms: 13 + -13 = 0 -13 + -7a + -6a2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(13 + 7a + 6a2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(13 + 7a + 6a2)' equal to zero and attempt to solve: Simplifying 13 + 7a + 6a2 = 0 Solving 13 + 7a + 6a2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 2.166666667 + 1.166666667a + a2 = 0 Move the constant term to the right: Add '-2.166666667' to each side of the equation. 2.166666667 + 1.166666667a + -2.166666667 + a2 = 0 + -2.166666667 Reorder the terms: 2.166666667 + -2.166666667 + 1.166666667a + a2 = 0 + -2.166666667 Combine like terms: 2.166666667 + -2.166666667 = 0.000000000 0.000000000 + 1.166666667a + a2 = 0 + -2.166666667 1.166666667a + a2 = 0 + -2.166666667 Combine like terms: 0 + -2.166666667 = -2.166666667 1.166666667a + a2 = -2.166666667 The a term is 1.166666667a. Take half its coefficient (0.5833333335). Square it (0.3402777780) and add it to both sides. Add '0.3402777780' to each side of the equation. 1.166666667a + 0.3402777780 + a2 = -2.166666667 + 0.3402777780 Reorder the terms: 0.3402777780 + 1.166666667a + a2 = -2.166666667 + 0.3402777780 Combine like terms: -2.166666667 + 0.3402777780 = -1.826388889 0.3402777780 + 1.166666667a + a2 = -1.826388889 Factor a perfect square on the left side: (a + 0.5833333335)(a + 0.5833333335) = -1.826388889 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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