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Simplifying 3x2 + -3x + -40 = 0 Reorder the terms: -40 + -3x + 3x2 = 0 Solving -40 + -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'. -13.33333333 + -1x + x2 = 0 Move the constant term to the right: Add '13.33333333' to each side of the equation. -13.33333333 + -1x + 13.33333333 + x2 = 0 + 13.33333333 Reorder the terms: -13.33333333 + 13.33333333 + -1x + x2 = 0 + 13.33333333 Combine like terms: -13.33333333 + 13.33333333 = 0.00000000 0.00000000 + -1x + x2 = 0 + 13.33333333 -1x + x2 = 0 + 13.33333333 Combine like terms: 0 + 13.33333333 = 13.33333333 -1x + x2 = 13.33333333 The x term is -1x. 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. -1x + 0.25 + x2 = 13.33333333 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 13.33333333 + 0.25 Combine like terms: 13.33333333 + 0.25 = 13.58333333 0.25 + -1x + x2 = 13.58333333 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 13.58333333 Calculate the square root of the right side: 3.685557397 Break this problem into two subproblems by setting (x + -0.5) equal to 3.685557397 and -3.685557397.Subproblem 1
x + -0.5 = 3.685557397 Simplifying x + -0.5 = 3.685557397 Reorder the terms: -0.5 + x = 3.685557397 Solving -0.5 + x = 3.685557397 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 = 3.685557397 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 3.685557397 + 0.5 x = 3.685557397 + 0.5 Combine like terms: 3.685557397 + 0.5 = 4.185557397 x = 4.185557397 Simplifying x = 4.185557397Subproblem 2
x + -0.5 = -3.685557397 Simplifying x + -0.5 = -3.685557397 Reorder the terms: -0.5 + x = -3.685557397 Solving -0.5 + x = -3.685557397 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 = -3.685557397 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -3.685557397 + 0.5 x = -3.685557397 + 0.5 Combine like terms: -3.685557397 + 0.5 = -3.185557397 x = -3.185557397 Simplifying x = -3.185557397Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.185557397, -3.185557397}
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