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Simplifying 2x + 3(2x2 + -15x + 18) = 0 Reorder the terms: 2x + 3(18 + -15x + 2x2) = 0 2x + (18 * 3 + -15x * 3 + 2x2 * 3) = 0 2x + (54 + -45x + 6x2) = 0 Reorder the terms: 54 + 2x + -45x + 6x2 = 0 Combine like terms: 2x + -45x = -43x 54 + -43x + 6x2 = 0 Solving 54 + -43x + 6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 9 + -7.166666667x + x2 = 0 Move the constant term to the right: Add '-9' to each side of the equation. 9 + -7.166666667x + -9 + x2 = 0 + -9 Reorder the terms: 9 + -9 + -7.166666667x + x2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -7.166666667x + x2 = 0 + -9 -7.166666667x + x2 = 0 + -9 Combine like terms: 0 + -9 = -9 -7.166666667x + x2 = -9 The x term is -7.166666667x. Take half its coefficient (-3.583333334). Square it (12.84027778) and add it to both sides. Add '12.84027778' to each side of the equation. -7.166666667x + 12.84027778 + x2 = -9 + 12.84027778 Reorder the terms: 12.84027778 + -7.166666667x + x2 = -9 + 12.84027778 Combine like terms: -9 + 12.84027778 = 3.84027778 12.84027778 + -7.166666667x + x2 = 3.84027778 Factor a perfect square on the left side: (x + -3.583333334)(x + -3.583333334) = 3.84027778 Calculate the square root of the right side: 1.95966267 Break this problem into two subproblems by setting (x + -3.583333334) equal to 1.95966267 and -1.95966267.Subproblem 1
x + -3.583333334 = 1.95966267 Simplifying x + -3.583333334 = 1.95966267 Reorder the terms: -3.583333334 + x = 1.95966267 Solving -3.583333334 + x = 1.95966267 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.583333334' to each side of the equation. -3.583333334 + 3.583333334 + x = 1.95966267 + 3.583333334 Combine like terms: -3.583333334 + 3.583333334 = 0.000000000 0.000000000 + x = 1.95966267 + 3.583333334 x = 1.95966267 + 3.583333334 Combine like terms: 1.95966267 + 3.583333334 = 5.542996004 x = 5.542996004 Simplifying x = 5.542996004Subproblem 2
x + -3.583333334 = -1.95966267 Simplifying x + -3.583333334 = -1.95966267 Reorder the terms: -3.583333334 + x = -1.95966267 Solving -3.583333334 + x = -1.95966267 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.583333334' to each side of the equation. -3.583333334 + 3.583333334 + x = -1.95966267 + 3.583333334 Combine like terms: -3.583333334 + 3.583333334 = 0.000000000 0.000000000 + x = -1.95966267 + 3.583333334 x = -1.95966267 + 3.583333334 Combine like terms: -1.95966267 + 3.583333334 = 1.623670664 x = 1.623670664 Simplifying x = 1.623670664Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.542996004, 1.623670664}
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