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Simplifying 3x2 + 3x + -34 = 0 Reorder the terms: -34 + 3x + 3x2 = 0 Solving -34 + 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'. -11.33333333 + x + x2 = 0 Move the constant term to the right: Add '11.33333333' to each side of the equation. -11.33333333 + x + 11.33333333 + x2 = 0 + 11.33333333 Reorder the terms: -11.33333333 + 11.33333333 + x + x2 = 0 + 11.33333333 Combine like terms: -11.33333333 + 11.33333333 = 0.00000000 0.00000000 + x + x2 = 0 + 11.33333333 x + x2 = 0 + 11.33333333 Combine like terms: 0 + 11.33333333 = 11.33333333 x + x2 = 11.33333333 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 = 11.33333333 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 11.33333333 + 0.25 Combine like terms: 11.33333333 + 0.25 = 11.58333333 1.25 + x2 = 11.58333333 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 11.58333333 Calculate the square root of the right side: 3.403429642 Break this problem into two subproblems by setting (x + 0.5) equal to 3.403429642 and -3.403429642.Subproblem 1
x + 0.5 = 3.403429642 Simplifying x + 0.5 = 3.403429642 Reorder the terms: 0.5 + x = 3.403429642 Solving 0.5 + x = 3.403429642 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 = 3.403429642 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 3.403429642 + -0.5 x = 3.403429642 + -0.5 Combine like terms: 3.403429642 + -0.5 = 2.903429642 x = 2.903429642 Simplifying x = 2.903429642Subproblem 2
x + 0.5 = -3.403429642 Simplifying x + 0.5 = -3.403429642 Reorder the terms: 0.5 + x = -3.403429642 Solving 0.5 + x = -3.403429642 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 = -3.403429642 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -3.403429642 + -0.5 x = -3.403429642 + -0.5 Combine like terms: -3.403429642 + -0.5 = -3.903429642 x = -3.903429642 Simplifying x = -3.903429642Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.903429642, -3.903429642}
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