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Simplifying 19a2 + 36a + -8 = 0 Reorder the terms: -8 + 36a + 19a2 = 0 Solving -8 + 36a + 19a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 19 the coefficient of the squared term: Divide each side by '19'. -0.4210526316 + 1.894736842a + a2 = 0 Move the constant term to the right: Add '0.4210526316' to each side of the equation. -0.4210526316 + 1.894736842a + 0.4210526316 + a2 = 0 + 0.4210526316 Reorder the terms: -0.4210526316 + 0.4210526316 + 1.894736842a + a2 = 0 + 0.4210526316 Combine like terms: -0.4210526316 + 0.4210526316 = 0.0000000000 0.0000000000 + 1.894736842a + a2 = 0 + 0.4210526316 1.894736842a + a2 = 0 + 0.4210526316 Combine like terms: 0 + 0.4210526316 = 0.4210526316 1.894736842a + a2 = 0.4210526316 The a term is 1.894736842a. Take half its coefficient (0.947368421). Square it (0.8975069251) and add it to both sides. Add '0.8975069251' to each side of the equation. 1.894736842a + 0.8975069251 + a2 = 0.4210526316 + 0.8975069251 Reorder the terms: 0.8975069251 + 1.894736842a + a2 = 0.4210526316 + 0.8975069251 Combine like terms: 0.4210526316 + 0.8975069251 = 1.3185595567 0.8975069251 + 1.894736842a + a2 = 1.3185595567 Factor a perfect square on the left side: (a + 0.947368421)(a + 0.947368421) = 1.3185595567 Calculate the square root of the right side: 1.148285486 Break this problem into two subproblems by setting (a + 0.947368421) equal to 1.148285486 and -1.148285486.Subproblem 1
a + 0.947368421 = 1.148285486 Simplifying a + 0.947368421 = 1.148285486 Reorder the terms: 0.947368421 + a = 1.148285486 Solving 0.947368421 + a = 1.148285486 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.947368421' to each side of the equation. 0.947368421 + -0.947368421 + a = 1.148285486 + -0.947368421 Combine like terms: 0.947368421 + -0.947368421 = 0.000000000 0.000000000 + a = 1.148285486 + -0.947368421 a = 1.148285486 + -0.947368421 Combine like terms: 1.148285486 + -0.947368421 = 0.200917065 a = 0.200917065 Simplifying a = 0.200917065Subproblem 2
a + 0.947368421 = -1.148285486 Simplifying a + 0.947368421 = -1.148285486 Reorder the terms: 0.947368421 + a = -1.148285486 Solving 0.947368421 + a = -1.148285486 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.947368421' to each side of the equation. 0.947368421 + -0.947368421 + a = -1.148285486 + -0.947368421 Combine like terms: 0.947368421 + -0.947368421 = 0.000000000 0.000000000 + a = -1.148285486 + -0.947368421 a = -1.148285486 + -0.947368421 Combine like terms: -1.148285486 + -0.947368421 = -2.095653907 a = -2.095653907 Simplifying a = -2.095653907Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.200917065, -2.095653907}
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