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Simplifying 3(2x + -3) * 9x + -4 = 2x + 12 Reorder the terms: 3(-3 + 2x) * 9x + -4 = 2x + 12 Reorder the terms for easier multiplication: 3 * 9x(-3 + 2x) + -4 = 2x + 12 Multiply 3 * 9 27x(-3 + 2x) + -4 = 2x + 12 (-3 * 27x + 2x * 27x) + -4 = 2x + 12 (-81x + 54x2) + -4 = 2x + 12 Reorder the terms: -4 + -81x + 54x2 = 2x + 12 Reorder the terms: -4 + -81x + 54x2 = 12 + 2x Solving -4 + -81x + 54x2 = 12 + 2x Solving for variable 'x'. Reorder the terms: -4 + -12 + -81x + -2x + 54x2 = 12 + 2x + -12 + -2x Combine like terms: -4 + -12 = -16 -16 + -81x + -2x + 54x2 = 12 + 2x + -12 + -2x Combine like terms: -81x + -2x = -83x -16 + -83x + 54x2 = 12 + 2x + -12 + -2x Reorder the terms: -16 + -83x + 54x2 = 12 + -12 + 2x + -2x Combine like terms: 12 + -12 = 0 -16 + -83x + 54x2 = 0 + 2x + -2x -16 + -83x + 54x2 = 2x + -2x Combine like terms: 2x + -2x = 0 -16 + -83x + 54x2 = 0 Begin completing the square. Divide all terms by 54 the coefficient of the squared term: Divide each side by '54'. -0.2962962963 + -1.537037037x + x2 = 0 Move the constant term to the right: Add '0.2962962963' to each side of the equation. -0.2962962963 + -1.537037037x + 0.2962962963 + x2 = 0 + 0.2962962963 Reorder the terms: -0.2962962963 + 0.2962962963 + -1.537037037x + x2 = 0 + 0.2962962963 Combine like terms: -0.2962962963 + 0.2962962963 = 0.0000000000 0.0000000000 + -1.537037037x + x2 = 0 + 0.2962962963 -1.537037037x + x2 = 0 + 0.2962962963 Combine like terms: 0 + 0.2962962963 = 0.2962962963 -1.537037037x + x2 = 0.2962962963 The x term is -1.537037037x. Take half its coefficient (-0.7685185185). Square it (0.5906207133) and add it to both sides. Add '0.5906207133' to each side of the equation. -1.537037037x + 0.5906207133 + x2 = 0.2962962963 + 0.5906207133 Reorder the terms: 0.5906207133 + -1.537037037x + x2 = 0.2962962963 + 0.5906207133 Combine like terms: 0.2962962963 + 0.5906207133 = 0.8869170096 0.5906207133 + -1.537037037x + x2 = 0.8869170096 Factor a perfect square on the left side: (x + -0.7685185185)(x + -0.7685185185) = 0.8869170096 Calculate the square root of the right side: 0.941762714 Break this problem into two subproblems by setting (x + -0.7685185185) equal to 0.941762714 and -0.941762714.Subproblem 1
x + -0.7685185185 = 0.941762714 Simplifying x + -0.7685185185 = 0.941762714 Reorder the terms: -0.7685185185 + x = 0.941762714 Solving -0.7685185185 + x = 0.941762714 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7685185185' to each side of the equation. -0.7685185185 + 0.7685185185 + x = 0.941762714 + 0.7685185185 Combine like terms: -0.7685185185 + 0.7685185185 = 0.0000000000 0.0000000000 + x = 0.941762714 + 0.7685185185 x = 0.941762714 + 0.7685185185 Combine like terms: 0.941762714 + 0.7685185185 = 1.7102812325 x = 1.7102812325 Simplifying x = 1.7102812325Subproblem 2
x + -0.7685185185 = -0.941762714 Simplifying x + -0.7685185185 = -0.941762714 Reorder the terms: -0.7685185185 + x = -0.941762714 Solving -0.7685185185 + x = -0.941762714 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7685185185' to each side of the equation. -0.7685185185 + 0.7685185185 + x = -0.941762714 + 0.7685185185 Combine like terms: -0.7685185185 + 0.7685185185 = 0.0000000000 0.0000000000 + x = -0.941762714 + 0.7685185185 x = -0.941762714 + 0.7685185185 Combine like terms: -0.941762714 + 0.7685185185 = -0.1732441955 x = -0.1732441955 Simplifying x = -0.1732441955Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.7102812325, -0.1732441955}
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