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Simplifying 2X2 + 31X + -6.1 = 0 Reorder the terms: -6.1 + 31X + 2X2 = 0 Solving -6.1 + 31X + 2X2 = 0 Solving for variable 'X'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -3.05 + 15.5X + X2 = 0 Move the constant term to the right: Add '3.05' to each side of the equation. -3.05 + 15.5X + 3.05 + X2 = 0 + 3.05 Reorder the terms: -3.05 + 3.05 + 15.5X + X2 = 0 + 3.05 Combine like terms: -3.05 + 3.05 = 0.00 0.00 + 15.5X + X2 = 0 + 3.05 15.5X + X2 = 0 + 3.05 Combine like terms: 0 + 3.05 = 3.05 15.5X + X2 = 3.05 The X term is 15.5X. Take half its coefficient (7.75). Square it (60.0625) and add it to both sides. Add '60.0625' to each side of the equation. 15.5X + 60.0625 + X2 = 3.05 + 60.0625 Reorder the terms: 60.0625 + 15.5X + X2 = 3.05 + 60.0625 Combine like terms: 3.05 + 60.0625 = 63.1125 60.0625 + 15.5X + X2 = 63.1125 Factor a perfect square on the left side: (X + 7.75)(X + 7.75) = 63.1125 Calculate the square root of the right side: 7.944337606 Break this problem into two subproblems by setting (X + 7.75) equal to 7.944337606 and -7.944337606.Subproblem 1
X + 7.75 = 7.944337606 Simplifying X + 7.75 = 7.944337606 Reorder the terms: 7.75 + X = 7.944337606 Solving 7.75 + X = 7.944337606 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-7.75' to each side of the equation. 7.75 + -7.75 + X = 7.944337606 + -7.75 Combine like terms: 7.75 + -7.75 = 0.00 0.00 + X = 7.944337606 + -7.75 X = 7.944337606 + -7.75 Combine like terms: 7.944337606 + -7.75 = 0.194337606 X = 0.194337606 Simplifying X = 0.194337606Subproblem 2
X + 7.75 = -7.944337606 Simplifying X + 7.75 = -7.944337606 Reorder the terms: 7.75 + X = -7.944337606 Solving 7.75 + X = -7.944337606 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-7.75' to each side of the equation. 7.75 + -7.75 + X = -7.944337606 + -7.75 Combine like terms: 7.75 + -7.75 = 0.00 0.00 + X = -7.944337606 + -7.75 X = -7.944337606 + -7.75 Combine like terms: -7.944337606 + -7.75 = -15.694337606 X = -15.694337606 Simplifying X = -15.694337606Solution
The solution to the problem is based on the solutions from the subproblems. X = {0.194337606, -15.694337606}
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