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Simplifying 77x2 + 124x + 29 = 0 Reorder the terms: 29 + 124x + 77x2 = 0 Solving 29 + 124x + 77x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 77 the coefficient of the squared term: Divide each side by '77'. 0.3766233766 + 1.61038961x + x2 = 0 Move the constant term to the right: Add '-0.3766233766' to each side of the equation. 0.3766233766 + 1.61038961x + -0.3766233766 + x2 = 0 + -0.3766233766 Reorder the terms: 0.3766233766 + -0.3766233766 + 1.61038961x + x2 = 0 + -0.3766233766 Combine like terms: 0.3766233766 + -0.3766233766 = 0.0000000000 0.0000000000 + 1.61038961x + x2 = 0 + -0.3766233766 1.61038961x + x2 = 0 + -0.3766233766 Combine like terms: 0 + -0.3766233766 = -0.3766233766 1.61038961x + x2 = -0.3766233766 The x term is 1.61038961x. Take half its coefficient (0.805194805). Square it (0.6483386740) and add it to both sides. Add '0.6483386740' to each side of the equation. 1.61038961x + 0.6483386740 + x2 = -0.3766233766 + 0.6483386740 Reorder the terms: 0.6483386740 + 1.61038961x + x2 = -0.3766233766 + 0.6483386740 Combine like terms: -0.3766233766 + 0.6483386740 = 0.2717152974 0.6483386740 + 1.61038961x + x2 = 0.2717152974 Factor a perfect square on the left side: (x + 0.805194805)(x + 0.805194805) = 0.2717152974 Calculate the square root of the right side: 0.521263175 Break this problem into two subproblems by setting (x + 0.805194805) equal to 0.521263175 and -0.521263175.Subproblem 1
x + 0.805194805 = 0.521263175 Simplifying x + 0.805194805 = 0.521263175 Reorder the terms: 0.805194805 + x = 0.521263175 Solving 0.805194805 + x = 0.521263175 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.805194805' to each side of the equation. 0.805194805 + -0.805194805 + x = 0.521263175 + -0.805194805 Combine like terms: 0.805194805 + -0.805194805 = 0.000000000 0.000000000 + x = 0.521263175 + -0.805194805 x = 0.521263175 + -0.805194805 Combine like terms: 0.521263175 + -0.805194805 = -0.28393163 x = -0.28393163 Simplifying x = -0.28393163Subproblem 2
x + 0.805194805 = -0.521263175 Simplifying x + 0.805194805 = -0.521263175 Reorder the terms: 0.805194805 + x = -0.521263175 Solving 0.805194805 + x = -0.521263175 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.805194805' to each side of the equation. 0.805194805 + -0.805194805 + x = -0.521263175 + -0.805194805 Combine like terms: 0.805194805 + -0.805194805 = 0.000000000 0.000000000 + x = -0.521263175 + -0.805194805 x = -0.521263175 + -0.805194805 Combine like terms: -0.521263175 + -0.805194805 = -1.32645798 x = -1.32645798 Simplifying x = -1.32645798Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.28393163, -1.32645798}
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