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Simplifying 3x * x = 6 + -2x Multiply x * x 3x2 = 6 + -2x Solving 3x2 = 6 + -2x Solving for variable 'x'. Reorder the terms: -6 + 2x + 3x2 = 6 + -2x + -6 + 2x Reorder the terms: -6 + 2x + 3x2 = 6 + -6 + -2x + 2x Combine like terms: 6 + -6 = 0 -6 + 2x + 3x2 = 0 + -2x + 2x -6 + 2x + 3x2 = -2x + 2x Combine like terms: -2x + 2x = 0 -6 + 2x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -2 + 0.6666666667x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 0.6666666667x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + 0.6666666667x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 0.6666666667x + x2 = 0 + 2 0.6666666667x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 0.6666666667x + x2 = 2 The x term is 0.6666666667x. Take half its coefficient (0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. 0.6666666667x + 0.1111111112 + x2 = 2 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667x + x2 = 2 + 0.1111111112 Combine like terms: 2 + 0.1111111112 = 2.1111111112 0.1111111112 + 0.6666666667x + x2 = 2.1111111112 Factor a perfect square on the left side: (x + 0.3333333334)(x + 0.3333333334) = 2.1111111112 Calculate the square root of the right side: 1.452966315 Break this problem into two subproblems by setting (x + 0.3333333334) equal to 1.452966315 and -1.452966315.Subproblem 1
x + 0.3333333334 = 1.452966315 Simplifying x + 0.3333333334 = 1.452966315 Reorder the terms: 0.3333333334 + x = 1.452966315 Solving 0.3333333334 + x = 1.452966315 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = 1.452966315 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = 1.452966315 + -0.3333333334 x = 1.452966315 + -0.3333333334 Combine like terms: 1.452966315 + -0.3333333334 = 1.1196329816 x = 1.1196329816 Simplifying x = 1.1196329816Subproblem 2
x + 0.3333333334 = -1.452966315 Simplifying x + 0.3333333334 = -1.452966315 Reorder the terms: 0.3333333334 + x = -1.452966315 Solving 0.3333333334 + x = -1.452966315 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = -1.452966315 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = -1.452966315 + -0.3333333334 x = -1.452966315 + -0.3333333334 Combine like terms: -1.452966315 + -0.3333333334 = -1.7862996484 x = -1.7862996484 Simplifying x = -1.7862996484Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.1196329816, -1.7862996484}
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