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Simplifying 6x2 + -183x + 350 = 0 Reorder the terms: 350 + -183x + 6x2 = 0 Solving 350 + -183x + 6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 58.33333333 + -30.5x + x2 = 0 Move the constant term to the right: Add '-58.33333333' to each side of the equation. 58.33333333 + -30.5x + -58.33333333 + x2 = 0 + -58.33333333 Reorder the terms: 58.33333333 + -58.33333333 + -30.5x + x2 = 0 + -58.33333333 Combine like terms: 58.33333333 + -58.33333333 = 0.00000000 0.00000000 + -30.5x + x2 = 0 + -58.33333333 -30.5x + x2 = 0 + -58.33333333 Combine like terms: 0 + -58.33333333 = -58.33333333 -30.5x + x2 = -58.33333333 The x term is -30.5x. Take half its coefficient (-15.25). Square it (232.5625) and add it to both sides. Add '232.5625' to each side of the equation. -30.5x + 232.5625 + x2 = -58.33333333 + 232.5625 Reorder the terms: 232.5625 + -30.5x + x2 = -58.33333333 + 232.5625 Combine like terms: -58.33333333 + 232.5625 = 174.22916667 232.5625 + -30.5x + x2 = 174.22916667 Factor a perfect square on the left side: (x + -15.25)(x + -15.25) = 174.22916667 Calculate the square root of the right side: 13.19958964 Break this problem into two subproblems by setting (x + -15.25) equal to 13.19958964 and -13.19958964.Subproblem 1
x + -15.25 = 13.19958964 Simplifying x + -15.25 = 13.19958964 Reorder the terms: -15.25 + x = 13.19958964 Solving -15.25 + x = 13.19958964 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15.25' to each side of the equation. -15.25 + 15.25 + x = 13.19958964 + 15.25 Combine like terms: -15.25 + 15.25 = 0.00 0.00 + x = 13.19958964 + 15.25 x = 13.19958964 + 15.25 Combine like terms: 13.19958964 + 15.25 = 28.44958964 x = 28.44958964 Simplifying x = 28.44958964Subproblem 2
x + -15.25 = -13.19958964 Simplifying x + -15.25 = -13.19958964 Reorder the terms: -15.25 + x = -13.19958964 Solving -15.25 + x = -13.19958964 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15.25' to each side of the equation. -15.25 + 15.25 + x = -13.19958964 + 15.25 Combine like terms: -15.25 + 15.25 = 0.00 0.00 + x = -13.19958964 + 15.25 x = -13.19958964 + 15.25 Combine like terms: -13.19958964 + 15.25 = 2.05041036 x = 2.05041036 Simplifying x = 2.05041036Solution
The solution to the problem is based on the solutions from the subproblems. x = {28.44958964, 2.05041036}
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