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Simplifying 23x + 37x(130 + -1x) = 3690 23x + (130 * 37x + -1x * 37x) = 3690 23x + (4810x + -37x2) = 3690 Combine like terms: 23x + 4810x = 4833x 4833x + -37x2 = 3690 Solving 4833x + -37x2 = 3690 Solving for variable 'x'. Reorder the terms: -3690 + 4833x + -37x2 = 3690 + -3690 Combine like terms: 3690 + -3690 = 0 -3690 + 4833x + -37x2 = 0 Begin completing the square. Divide all terms by -37 the coefficient of the squared term: Divide each side by '-37'. 99.72972973 + -130.6216216x + x2 = 0 Move the constant term to the right: Add '-99.72972973' to each side of the equation. 99.72972973 + -130.6216216x + -99.72972973 + x2 = 0 + -99.72972973 Reorder the terms: 99.72972973 + -99.72972973 + -130.6216216x + x2 = 0 + -99.72972973 Combine like terms: 99.72972973 + -99.72972973 = 0.00000000 0.00000000 + -130.6216216x + x2 = 0 + -99.72972973 -130.6216216x + x2 = 0 + -99.72972973 Combine like terms: 0 + -99.72972973 = -99.72972973 -130.6216216x + x2 = -99.72972973 The x term is -130.6216216x. Take half its coefficient (-65.3108108). Square it (4265.502007) and add it to both sides. Add '4265.502007' to each side of the equation. -130.6216216x + 4265.502007 + x2 = -99.72972973 + 4265.502007 Reorder the terms: 4265.502007 + -130.6216216x + x2 = -99.72972973 + 4265.502007 Combine like terms: -99.72972973 + 4265.502007 = 4165.77227727 4265.502007 + -130.6216216x + x2 = 4165.77227727 Factor a perfect square on the left side: (x + -65.3108108)(x + -65.3108108) = 4165.77227727 Calculate the square root of the right side: 64.542794154 Break this problem into two subproblems by setting (x + -65.3108108) equal to 64.542794154 and -64.542794154.Subproblem 1
x + -65.3108108 = 64.542794154 Simplifying x + -65.3108108 = 64.542794154 Reorder the terms: -65.3108108 + x = 64.542794154 Solving -65.3108108 + x = 64.542794154 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '65.3108108' to each side of the equation. -65.3108108 + 65.3108108 + x = 64.542794154 + 65.3108108 Combine like terms: -65.3108108 + 65.3108108 = 0.0000000 0.0000000 + x = 64.542794154 + 65.3108108 x = 64.542794154 + 65.3108108 Combine like terms: 64.542794154 + 65.3108108 = 129.853604954 x = 129.853604954 Simplifying x = 129.853604954Subproblem 2
x + -65.3108108 = -64.542794154 Simplifying x + -65.3108108 = -64.542794154 Reorder the terms: -65.3108108 + x = -64.542794154 Solving -65.3108108 + x = -64.542794154 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '65.3108108' to each side of the equation. -65.3108108 + 65.3108108 + x = -64.542794154 + 65.3108108 Combine like terms: -65.3108108 + 65.3108108 = 0.0000000 0.0000000 + x = -64.542794154 + 65.3108108 x = -64.542794154 + 65.3108108 Combine like terms: -64.542794154 + 65.3108108 = 0.768016646 x = 0.768016646 Simplifying x = 0.768016646Solution
The solution to the problem is based on the solutions from the subproblems. x = {129.853604954, 0.768016646}
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