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Simplifying 3x2 + 3x + -754 = 0 Reorder the terms: -754 + 3x + 3x2 = 0 Solving -754 + 3x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -251.3333333 + x + x2 = 0 Move the constant term to the right: Add '251.3333333' to each side of the equation. -251.3333333 + x + 251.3333333 + x2 = 0 + 251.3333333 Reorder the terms: -251.3333333 + 251.3333333 + x + x2 = 0 + 251.3333333 Combine like terms: -251.3333333 + 251.3333333 = 0.0000000 0.0000000 + x + x2 = 0 + 251.3333333 x + x2 = 0 + 251.3333333 Combine like terms: 0 + 251.3333333 = 251.3333333 x + x2 = 251.3333333 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 251.3333333 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 251.3333333 + 0.25 Combine like terms: 251.3333333 + 0.25 = 251.5833333 1.25 + x2 = 251.5833333 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 251.5833333 Calculate the square root of the right side: 15.86137867 Break this problem into two subproblems by setting (x + 0.5) equal to 15.86137867 and -15.86137867.Subproblem 1
x + 0.5 = 15.86137867 Simplifying x + 0.5 = 15.86137867 Reorder the terms: 0.5 + x = 15.86137867 Solving 0.5 + x = 15.86137867 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 15.86137867 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 15.86137867 + -0.5 x = 15.86137867 + -0.5 Combine like terms: 15.86137867 + -0.5 = 15.36137867 x = 15.36137867 Simplifying x = 15.36137867Subproblem 2
x + 0.5 = -15.86137867 Simplifying x + 0.5 = -15.86137867 Reorder the terms: 0.5 + x = -15.86137867 Solving 0.5 + x = -15.86137867 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -15.86137867 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -15.86137867 + -0.5 x = -15.86137867 + -0.5 Combine like terms: -15.86137867 + -0.5 = -16.36137867 x = -16.36137867 Simplifying x = -16.36137867Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.36137867, -16.36137867}
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