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Simplifying 6x2 + 40x = 9x + 5 Reorder the terms: 40x + 6x2 = 9x + 5 Reorder the terms: 40x + 6x2 = 5 + 9x Solving 40x + 6x2 = 5 + 9x Solving for variable 'x'. Reorder the terms: -5 + 40x + -9x + 6x2 = 5 + 9x + -5 + -9x Combine like terms: 40x + -9x = 31x -5 + 31x + 6x2 = 5 + 9x + -5 + -9x Reorder the terms: -5 + 31x + 6x2 = 5 + -5 + 9x + -9x Combine like terms: 5 + -5 = 0 -5 + 31x + 6x2 = 0 + 9x + -9x -5 + 31x + 6x2 = 9x + -9x Combine like terms: 9x + -9x = 0 -5 + 31x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -0.8333333333 + 5.166666667x + x2 = 0 Move the constant term to the right: Add '0.8333333333' to each side of the equation. -0.8333333333 + 5.166666667x + 0.8333333333 + x2 = 0 + 0.8333333333 Reorder the terms: -0.8333333333 + 0.8333333333 + 5.166666667x + x2 = 0 + 0.8333333333 Combine like terms: -0.8333333333 + 0.8333333333 = 0.0000000000 0.0000000000 + 5.166666667x + x2 = 0 + 0.8333333333 5.166666667x + x2 = 0 + 0.8333333333 Combine like terms: 0 + 0.8333333333 = 0.8333333333 5.166666667x + x2 = 0.8333333333 The x term is 5.166666667x. Take half its coefficient (2.583333334). Square it (6.673611115) and add it to both sides. Add '6.673611115' to each side of the equation. 5.166666667x + 6.673611115 + x2 = 0.8333333333 + 6.673611115 Reorder the terms: 6.673611115 + 5.166666667x + x2 = 0.8333333333 + 6.673611115 Combine like terms: 0.8333333333 + 6.673611115 = 7.5069444483 6.673611115 + 5.166666667x + x2 = 7.5069444483 Factor a perfect square on the left side: (x + 2.583333334)(x + 2.583333334) = 7.5069444483 Calculate the square root of the right side: 2.739880371 Break this problem into two subproblems by setting (x + 2.583333334) equal to 2.739880371 and -2.739880371.Subproblem 1
x + 2.583333334 = 2.739880371 Simplifying x + 2.583333334 = 2.739880371 Reorder the terms: 2.583333334 + x = 2.739880371 Solving 2.583333334 + x = 2.739880371 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.583333334' to each side of the equation. 2.583333334 + -2.583333334 + x = 2.739880371 + -2.583333334 Combine like terms: 2.583333334 + -2.583333334 = 0.000000000 0.000000000 + x = 2.739880371 + -2.583333334 x = 2.739880371 + -2.583333334 Combine like terms: 2.739880371 + -2.583333334 = 0.156547037 x = 0.156547037 Simplifying x = 0.156547037Subproblem 2
x + 2.583333334 = -2.739880371 Simplifying x + 2.583333334 = -2.739880371 Reorder the terms: 2.583333334 + x = -2.739880371 Solving 2.583333334 + x = -2.739880371 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.583333334' to each side of the equation. 2.583333334 + -2.583333334 + x = -2.739880371 + -2.583333334 Combine like terms: 2.583333334 + -2.583333334 = 0.000000000 0.000000000 + x = -2.739880371 + -2.583333334 x = -2.739880371 + -2.583333334 Combine like terms: -2.739880371 + -2.583333334 = -5.323213705 x = -5.323213705 Simplifying x = -5.323213705Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.156547037, -5.323213705}
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