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Simplifying 61x2 + 56x + 4 = 0 Reorder the terms: 4 + 56x + 61x2 = 0 Solving 4 + 56x + 61x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 61 the coefficient of the squared term: Divide each side by '61'. 0.06557377049 + 0.9180327869x + x2 = 0 Move the constant term to the right: Add '-0.06557377049' to each side of the equation. 0.06557377049 + 0.9180327869x + -0.06557377049 + x2 = 0 + -0.06557377049 Reorder the terms: 0.06557377049 + -0.06557377049 + 0.9180327869x + x2 = 0 + -0.06557377049 Combine like terms: 0.06557377049 + -0.06557377049 = 0.00000000000 0.00000000000 + 0.9180327869x + x2 = 0 + -0.06557377049 0.9180327869x + x2 = 0 + -0.06557377049 Combine like terms: 0 + -0.06557377049 = -0.06557377049 0.9180327869x + x2 = -0.06557377049 The x term is 0.9180327869x. Take half its coefficient (0.4590163935). Square it (0.2106960495) and add it to both sides. Add '0.2106960495' to each side of the equation. 0.9180327869x + 0.2106960495 + x2 = -0.06557377049 + 0.2106960495 Reorder the terms: 0.2106960495 + 0.9180327869x + x2 = -0.06557377049 + 0.2106960495 Combine like terms: -0.06557377049 + 0.2106960495 = 0.14512227901 0.2106960495 + 0.9180327869x + x2 = 0.14512227901 Factor a perfect square on the left side: (x + 0.4590163935)(x + 0.4590163935) = 0.14512227901 Calculate the square root of the right side: 0.380949182 Break this problem into two subproblems by setting (x + 0.4590163935) equal to 0.380949182 and -0.380949182.Subproblem 1
x + 0.4590163935 = 0.380949182 Simplifying x + 0.4590163935 = 0.380949182 Reorder the terms: 0.4590163935 + x = 0.380949182 Solving 0.4590163935 + x = 0.380949182 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4590163935' to each side of the equation. 0.4590163935 + -0.4590163935 + x = 0.380949182 + -0.4590163935 Combine like terms: 0.4590163935 + -0.4590163935 = 0.0000000000 0.0000000000 + x = 0.380949182 + -0.4590163935 x = 0.380949182 + -0.4590163935 Combine like terms: 0.380949182 + -0.4590163935 = -0.0780672115 x = -0.0780672115 Simplifying x = -0.0780672115Subproblem 2
x + 0.4590163935 = -0.380949182 Simplifying x + 0.4590163935 = -0.380949182 Reorder the terms: 0.4590163935 + x = -0.380949182 Solving 0.4590163935 + x = -0.380949182 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4590163935' to each side of the equation. 0.4590163935 + -0.4590163935 + x = -0.380949182 + -0.4590163935 Combine like terms: 0.4590163935 + -0.4590163935 = 0.0000000000 0.0000000000 + x = -0.380949182 + -0.4590163935 x = -0.380949182 + -0.4590163935 Combine like terms: -0.380949182 + -0.4590163935 = -0.8399655755 x = -0.8399655755 Simplifying x = -0.8399655755Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.0780672115, -0.8399655755}
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