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Simplifying 125x + -133 = 3x(2 + -1x) Reorder the terms: -133 + 125x = 3x(2 + -1x) -133 + 125x = (2 * 3x + -1x * 3x) -133 + 125x = (6x + -3x2) Solving -133 + 125x = 6x + -3x2 Solving for variable 'x'. Combine like terms: 125x + -6x = 119x -133 + 119x + 3x2 = 6x + -3x2 + -6x + 3x2 Reorder the terms: -133 + 119x + 3x2 = 6x + -6x + -3x2 + 3x2 Combine like terms: 6x + -6x = 0 -133 + 119x + 3x2 = 0 + -3x2 + 3x2 -133 + 119x + 3x2 = -3x2 + 3x2 Combine like terms: -3x2 + 3x2 = 0 -133 + 119x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -44.33333333 + 39.66666667x + x2 = 0 Move the constant term to the right: Add '44.33333333' to each side of the equation. -44.33333333 + 39.66666667x + 44.33333333 + x2 = 0 + 44.33333333 Reorder the terms: -44.33333333 + 44.33333333 + 39.66666667x + x2 = 0 + 44.33333333 Combine like terms: -44.33333333 + 44.33333333 = 0.00000000 0.00000000 + 39.66666667x + x2 = 0 + 44.33333333 39.66666667x + x2 = 0 + 44.33333333 Combine like terms: 0 + 44.33333333 = 44.33333333 39.66666667x + x2 = 44.33333333 The x term is 39.66666667x. Take half its coefficient (19.83333334). Square it (393.3611114) and add it to both sides. Add '393.3611114' to each side of the equation. 39.66666667x + 393.3611114 + x2 = 44.33333333 + 393.3611114 Reorder the terms: 393.3611114 + 39.66666667x + x2 = 44.33333333 + 393.3611114 Combine like terms: 44.33333333 + 393.3611114 = 437.69444473 393.3611114 + 39.66666667x + x2 = 437.69444473 Factor a perfect square on the left side: (x + 19.83333334)(x + 19.83333334) = 437.69444473 Calculate the square root of the right side: 20.921148265 Break this problem into two subproblems by setting (x + 19.83333334) equal to 20.921148265 and -20.921148265.Subproblem 1
x + 19.83333334 = 20.921148265 Simplifying x + 19.83333334 = 20.921148265 Reorder the terms: 19.83333334 + x = 20.921148265 Solving 19.83333334 + x = 20.921148265 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-19.83333334' to each side of the equation. 19.83333334 + -19.83333334 + x = 20.921148265 + -19.83333334 Combine like terms: 19.83333334 + -19.83333334 = 0.00000000 0.00000000 + x = 20.921148265 + -19.83333334 x = 20.921148265 + -19.83333334 Combine like terms: 20.921148265 + -19.83333334 = 1.087814925 x = 1.087814925 Simplifying x = 1.087814925Subproblem 2
x + 19.83333334 = -20.921148265 Simplifying x + 19.83333334 = -20.921148265 Reorder the terms: 19.83333334 + x = -20.921148265 Solving 19.83333334 + x = -20.921148265 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-19.83333334' to each side of the equation. 19.83333334 + -19.83333334 + x = -20.921148265 + -19.83333334 Combine like terms: 19.83333334 + -19.83333334 = 0.00000000 0.00000000 + x = -20.921148265 + -19.83333334 x = -20.921148265 + -19.83333334 Combine like terms: -20.921148265 + -19.83333334 = -40.754481605 x = -40.754481605 Simplifying x = -40.754481605Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.087814925, -40.754481605}
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