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Simplifying 54x2 + 33x + 1 = 0 Reorder the terms: 1 + 33x + 54x2 = 0 Solving 1 + 33x + 54x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 54 the coefficient of the squared term: Divide each side by '54'. 0.01851851852 + 0.6111111111x + x2 = 0 Move the constant term to the right: Add '-0.01851851852' to each side of the equation. 0.01851851852 + 0.6111111111x + -0.01851851852 + x2 = 0 + -0.01851851852 Reorder the terms: 0.01851851852 + -0.01851851852 + 0.6111111111x + x2 = 0 + -0.01851851852 Combine like terms: 0.01851851852 + -0.01851851852 = 0.00000000000 0.00000000000 + 0.6111111111x + x2 = 0 + -0.01851851852 0.6111111111x + x2 = 0 + -0.01851851852 Combine like terms: 0 + -0.01851851852 = -0.01851851852 0.6111111111x + x2 = -0.01851851852 The x term is 0.6111111111x. Take half its coefficient (0.3055555556). Square it (0.09336419756) and add it to both sides. Add '0.09336419756' to each side of the equation. 0.6111111111x + 0.09336419756 + x2 = -0.01851851852 + 0.09336419756 Reorder the terms: 0.09336419756 + 0.6111111111x + x2 = -0.01851851852 + 0.09336419756 Combine like terms: -0.01851851852 + 0.09336419756 = 0.07484567904 0.09336419756 + 0.6111111111x + x2 = 0.07484567904 Factor a perfect square on the left side: (x + 0.3055555556)(x + 0.3055555556) = 0.07484567904 Calculate the square root of the right side: 0.273579383 Break this problem into two subproblems by setting (x + 0.3055555556) equal to 0.273579383 and -0.273579383.Subproblem 1
x + 0.3055555556 = 0.273579383 Simplifying x + 0.3055555556 = 0.273579383 Reorder the terms: 0.3055555556 + x = 0.273579383 Solving 0.3055555556 + x = 0.273579383 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3055555556' to each side of the equation. 0.3055555556 + -0.3055555556 + x = 0.273579383 + -0.3055555556 Combine like terms: 0.3055555556 + -0.3055555556 = 0.0000000000 0.0000000000 + x = 0.273579383 + -0.3055555556 x = 0.273579383 + -0.3055555556 Combine like terms: 0.273579383 + -0.3055555556 = -0.0319761726 x = -0.0319761726 Simplifying x = -0.0319761726Subproblem 2
x + 0.3055555556 = -0.273579383 Simplifying x + 0.3055555556 = -0.273579383 Reorder the terms: 0.3055555556 + x = -0.273579383 Solving 0.3055555556 + x = -0.273579383 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3055555556' to each side of the equation. 0.3055555556 + -0.3055555556 + x = -0.273579383 + -0.3055555556 Combine like terms: 0.3055555556 + -0.3055555556 = 0.0000000000 0.0000000000 + x = -0.273579383 + -0.3055555556 x = -0.273579383 + -0.3055555556 Combine like terms: -0.273579383 + -0.3055555556 = -0.5791349386 x = -0.5791349386 Simplifying x = -0.5791349386Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.0319761726, -0.5791349386}
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