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Simplifying 36a2 + 34a + 40 = 0 Reorder the terms: 40 + 34a + 36a2 = 0 Solving 40 + 34a + 36a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '2'. 2(20 + 17a + 18a2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(20 + 17a + 18a2)' equal to zero and attempt to solve: Simplifying 20 + 17a + 18a2 = 0 Solving 20 + 17a + 18a2 = 0 Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. 1.111111111 + 0.9444444444a + a2 = 0 Move the constant term to the right: Add '-1.111111111' to each side of the equation. 1.111111111 + 0.9444444444a + -1.111111111 + a2 = 0 + -1.111111111 Reorder the terms: 1.111111111 + -1.111111111 + 0.9444444444a + a2 = 0 + -1.111111111 Combine like terms: 1.111111111 + -1.111111111 = 0.000000000 0.000000000 + 0.9444444444a + a2 = 0 + -1.111111111 0.9444444444a + a2 = 0 + -1.111111111 Combine like terms: 0 + -1.111111111 = -1.111111111 0.9444444444a + a2 = -1.111111111 The a term is 0.9444444444a. Take half its coefficient (0.4722222222). Square it (0.2229938271) and add it to both sides. Add '0.2229938271' to each side of the equation. 0.9444444444a + 0.2229938271 + a2 = -1.111111111 + 0.2229938271 Reorder the terms: 0.2229938271 + 0.9444444444a + a2 = -1.111111111 + 0.2229938271 Combine like terms: -1.111111111 + 0.2229938271 = -0.8881172839 0.2229938271 + 0.9444444444a + a2 = -0.8881172839 Factor a perfect square on the left side: (a + 0.4722222222)(a + 0.4722222222) = -0.8881172839 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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