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Simplifying 6x(2x + 2) = x + 2 Reorder the terms: 6x(2 + 2x) = x + 2 (2 * 6x + 2x * 6x) = x + 2 (12x + 12x2) = x + 2 Reorder the terms: 12x + 12x2 = 2 + x Solving 12x + 12x2 = 2 + x Solving for variable 'x'. Reorder the terms: -2 + 12x + -1x + 12x2 = 2 + x + -2 + -1x Combine like terms: 12x + -1x = 11x -2 + 11x + 12x2 = 2 + x + -2 + -1x Reorder the terms: -2 + 11x + 12x2 = 2 + -2 + x + -1x Combine like terms: 2 + -2 = 0 -2 + 11x + 12x2 = 0 + x + -1x -2 + 11x + 12x2 = x + -1x Combine like terms: x + -1x = 0 -2 + 11x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -0.1666666667 + 0.9166666667x + x2 = 0 Move the constant term to the right: Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.9166666667x + 0.1666666667 + x2 = 0 + 0.1666666667 Reorder the terms: -0.1666666667 + 0.1666666667 + 0.9166666667x + x2 = 0 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + 0.9166666667x + x2 = 0 + 0.1666666667 0.9166666667x + x2 = 0 + 0.1666666667 Combine like terms: 0 + 0.1666666667 = 0.1666666667 0.9166666667x + x2 = 0.1666666667 The x term is 0.9166666667x. Take half its coefficient (0.4583333334). Square it (0.2100694445) and add it to both sides. Add '0.2100694445' to each side of the equation. 0.9166666667x + 0.2100694445 + x2 = 0.1666666667 + 0.2100694445 Reorder the terms: 0.2100694445 + 0.9166666667x + x2 = 0.1666666667 + 0.2100694445 Combine like terms: 0.1666666667 + 0.2100694445 = 0.3767361112 0.2100694445 + 0.9166666667x + x2 = 0.3767361112 Factor a perfect square on the left side: (x + 0.4583333334)(x + 0.4583333334) = 0.3767361112 Calculate the square root of the right side: 0.613788328 Break this problem into two subproblems by setting (x + 0.4583333334) equal to 0.613788328 and -0.613788328.Subproblem 1
x + 0.4583333334 = 0.613788328 Simplifying x + 0.4583333334 = 0.613788328 Reorder the terms: 0.4583333334 + x = 0.613788328 Solving 0.4583333334 + x = 0.613788328 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4583333334' to each side of the equation. 0.4583333334 + -0.4583333334 + x = 0.613788328 + -0.4583333334 Combine like terms: 0.4583333334 + -0.4583333334 = 0.0000000000 0.0000000000 + x = 0.613788328 + -0.4583333334 x = 0.613788328 + -0.4583333334 Combine like terms: 0.613788328 + -0.4583333334 = 0.1554549946 x = 0.1554549946 Simplifying x = 0.1554549946Subproblem 2
x + 0.4583333334 = -0.613788328 Simplifying x + 0.4583333334 = -0.613788328 Reorder the terms: 0.4583333334 + x = -0.613788328 Solving 0.4583333334 + x = -0.613788328 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4583333334' to each side of the equation. 0.4583333334 + -0.4583333334 + x = -0.613788328 + -0.4583333334 Combine like terms: 0.4583333334 + -0.4583333334 = 0.0000000000 0.0000000000 + x = -0.613788328 + -0.4583333334 x = -0.613788328 + -0.4583333334 Combine like terms: -0.613788328 + -0.4583333334 = -1.0721216614 x = -1.0721216614 Simplifying x = -1.0721216614Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.1554549946, -1.0721216614}
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