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Simplifying 3x(2x + -9) + (2x + -9) = 360 Reorder the terms: 3x(-9 + 2x) + (2x + -9) = 360 (-9 * 3x + 2x * 3x) + (2x + -9) = 360 (-27x + 6x2) + (2x + -9) = 360 Reorder the terms: -27x + 6x2 + (-9 + 2x) = 360 Remove parenthesis around (-9 + 2x) -27x + 6x2 + -9 + 2x = 360 Reorder the terms: -9 + -27x + 2x + 6x2 = 360 Combine like terms: -27x + 2x = -25x -9 + -25x + 6x2 = 360 Solving -9 + -25x + 6x2 = 360 Solving for variable 'x'. Reorder the terms: -9 + -360 + -25x + 6x2 = 360 + -360 Combine like terms: -9 + -360 = -369 -369 + -25x + 6x2 = 360 + -360 Combine like terms: 360 + -360 = 0 -369 + -25x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -61.5 + -4.166666667x + x2 = 0 Move the constant term to the right: Add '61.5' to each side of the equation. -61.5 + -4.166666667x + 61.5 + x2 = 0 + 61.5 Reorder the terms: -61.5 + 61.5 + -4.166666667x + x2 = 0 + 61.5 Combine like terms: -61.5 + 61.5 = 0.0 0.0 + -4.166666667x + x2 = 0 + 61.5 -4.166666667x + x2 = 0 + 61.5 Combine like terms: 0 + 61.5 = 61.5 -4.166666667x + x2 = 61.5 The x term is -4.166666667x. Take half its coefficient (-2.083333334). Square it (4.340277781) and add it to both sides. Add '4.340277781' to each side of the equation. -4.166666667x + 4.340277781 + x2 = 61.5 + 4.340277781 Reorder the terms: 4.340277781 + -4.166666667x + x2 = 61.5 + 4.340277781 Combine like terms: 61.5 + 4.340277781 = 65.840277781 4.340277781 + -4.166666667x + x2 = 65.840277781 Factor a perfect square on the left side: (x + -2.083333334)(x + -2.083333334) = 65.840277781 Calculate the square root of the right side: 8.114202227 Break this problem into two subproblems by setting (x + -2.083333334) equal to 8.114202227 and -8.114202227.Subproblem 1
x + -2.083333334 = 8.114202227 Simplifying x + -2.083333334 = 8.114202227 Reorder the terms: -2.083333334 + x = 8.114202227 Solving -2.083333334 + x = 8.114202227 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.083333334' to each side of the equation. -2.083333334 + 2.083333334 + x = 8.114202227 + 2.083333334 Combine like terms: -2.083333334 + 2.083333334 = 0.000000000 0.000000000 + x = 8.114202227 + 2.083333334 x = 8.114202227 + 2.083333334 Combine like terms: 8.114202227 + 2.083333334 = 10.197535561 x = 10.197535561 Simplifying x = 10.197535561Subproblem 2
x + -2.083333334 = -8.114202227 Simplifying x + -2.083333334 = -8.114202227 Reorder the terms: -2.083333334 + x = -8.114202227 Solving -2.083333334 + x = -8.114202227 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.083333334' to each side of the equation. -2.083333334 + 2.083333334 + x = -8.114202227 + 2.083333334 Combine like terms: -2.083333334 + 2.083333334 = 0.000000000 0.000000000 + x = -8.114202227 + 2.083333334 x = -8.114202227 + 2.083333334 Combine like terms: -8.114202227 + 2.083333334 = -6.030868893 x = -6.030868893 Simplifying x = -6.030868893Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.197535561, -6.030868893}
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