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Simplifying 6x2 + 3x = 25x + 275 Reorder the terms: 3x + 6x2 = 25x + 275 Reorder the terms: 3x + 6x2 = 275 + 25x Solving 3x + 6x2 = 275 + 25x Solving for variable 'x'. Reorder the terms: -275 + 3x + -25x + 6x2 = 275 + 25x + -275 + -25x Combine like terms: 3x + -25x = -22x -275 + -22x + 6x2 = 275 + 25x + -275 + -25x Reorder the terms: -275 + -22x + 6x2 = 275 + -275 + 25x + -25x Combine like terms: 275 + -275 = 0 -275 + -22x + 6x2 = 0 + 25x + -25x -275 + -22x + 6x2 = 25x + -25x Combine like terms: 25x + -25x = 0 -275 + -22x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -45.83333333 + -3.666666667x + x2 = 0 Move the constant term to the right: Add '45.83333333' to each side of the equation. -45.83333333 + -3.666666667x + 45.83333333 + x2 = 0 + 45.83333333 Reorder the terms: -45.83333333 + 45.83333333 + -3.666666667x + x2 = 0 + 45.83333333 Combine like terms: -45.83333333 + 45.83333333 = 0.00000000 0.00000000 + -3.666666667x + x2 = 0 + 45.83333333 -3.666666667x + x2 = 0 + 45.83333333 Combine like terms: 0 + 45.83333333 = 45.83333333 -3.666666667x + x2 = 45.83333333 The x term is -3.666666667x. Take half its coefficient (-1.833333334). Square it (3.361111114) and add it to both sides. Add '3.361111114' to each side of the equation. -3.666666667x + 3.361111114 + x2 = 45.83333333 + 3.361111114 Reorder the terms: 3.361111114 + -3.666666667x + x2 = 45.83333333 + 3.361111114 Combine like terms: 45.83333333 + 3.361111114 = 49.194444444 3.361111114 + -3.666666667x + x2 = 49.194444444 Factor a perfect square on the left side: (x + -1.833333334)(x + -1.833333334) = 49.194444444 Calculate the square root of the right side: 7.013875137 Break this problem into two subproblems by setting (x + -1.833333334) equal to 7.013875137 and -7.013875137.Subproblem 1
x + -1.833333334 = 7.013875137 Simplifying x + -1.833333334 = 7.013875137 Reorder the terms: -1.833333334 + x = 7.013875137 Solving -1.833333334 + x = 7.013875137 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.833333334' to each side of the equation. -1.833333334 + 1.833333334 + x = 7.013875137 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + x = 7.013875137 + 1.833333334 x = 7.013875137 + 1.833333334 Combine like terms: 7.013875137 + 1.833333334 = 8.847208471 x = 8.847208471 Simplifying x = 8.847208471Subproblem 2
x + -1.833333334 = -7.013875137 Simplifying x + -1.833333334 = -7.013875137 Reorder the terms: -1.833333334 + x = -7.013875137 Solving -1.833333334 + x = -7.013875137 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.833333334' to each side of the equation. -1.833333334 + 1.833333334 + x = -7.013875137 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + x = -7.013875137 + 1.833333334 x = -7.013875137 + 1.833333334 Combine like terms: -7.013875137 + 1.833333334 = -5.180541803 x = -5.180541803 Simplifying x = -5.180541803Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.847208471, -5.180541803}
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