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Simplifying x(138 + -1x) = 126 (138 * x + -1x * x) = 126 (138x + -1x2) = 126 Solving 138x + -1x2 = 126 Solving for variable 'x'. Reorder the terms: -126 + 138x + -1x2 = 126 + -126 Combine like terms: 126 + -126 = 0 -126 + 138x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 126 + -138x + x2 = 0 Move the constant term to the right: Add '-126' to each side of the equation. 126 + -138x + -126 + x2 = 0 + -126 Reorder the terms: 126 + -126 + -138x + x2 = 0 + -126 Combine like terms: 126 + -126 = 0 0 + -138x + x2 = 0 + -126 -138x + x2 = 0 + -126 Combine like terms: 0 + -126 = -126 -138x + x2 = -126 The x term is -138x. Take half its coefficient (-69). Square it (4761) and add it to both sides. Add '4761' to each side of the equation. -138x + 4761 + x2 = -126 + 4761 Reorder the terms: 4761 + -138x + x2 = -126 + 4761 Combine like terms: -126 + 4761 = 4635 4761 + -138x + x2 = 4635 Factor a perfect square on the left side: (x + -69)(x + -69) = 4635 Calculate the square root of the right side: 68.080834307 Break this problem into two subproblems by setting (x + -69) equal to 68.080834307 and -68.080834307.Subproblem 1
x + -69 = 68.080834307 Simplifying x + -69 = 68.080834307 Reorder the terms: -69 + x = 68.080834307 Solving -69 + x = 68.080834307 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '69' to each side of the equation. -69 + 69 + x = 68.080834307 + 69 Combine like terms: -69 + 69 = 0 0 + x = 68.080834307 + 69 x = 68.080834307 + 69 Combine like terms: 68.080834307 + 69 = 137.080834307 x = 137.080834307 Simplifying x = 137.080834307Subproblem 2
x + -69 = -68.080834307 Simplifying x + -69 = -68.080834307 Reorder the terms: -69 + x = -68.080834307 Solving -69 + x = -68.080834307 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '69' to each side of the equation. -69 + 69 + x = -68.080834307 + 69 Combine like terms: -69 + 69 = 0 0 + x = -68.080834307 + 69 x = -68.080834307 + 69 Combine like terms: -68.080834307 + 69 = 0.919165693 x = 0.919165693 Simplifying x = 0.919165693Solution
The solution to the problem is based on the solutions from the subproblems. x = {137.080834307, 0.919165693}
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