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Simplifying (x2 + 3x + 2) + -1(3x2 + -6x + 4) = 0 Reorder the terms: (2 + 3x + x2) + -1(3x2 + -6x + 4) = 0 Remove parenthesis around (2 + 3x + x2) 2 + 3x + x2 + -1(3x2 + -6x + 4) = 0 Reorder the terms: 2 + 3x + x2 + -1(4 + -6x + 3x2) = 0 2 + 3x + x2 + (4 * -1 + -6x * -1 + 3x2 * -1) = 0 2 + 3x + x2 + (-4 + 6x + -3x2) = 0 Reorder the terms: 2 + -4 + 3x + 6x + x2 + -3x2 = 0 Combine like terms: 2 + -4 = -2 -2 + 3x + 6x + x2 + -3x2 = 0 Combine like terms: 3x + 6x = 9x -2 + 9x + x2 + -3x2 = 0 Combine like terms: x2 + -3x2 = -2x2 -2 + 9x + -2x2 = 0 Solving -2 + 9x + -2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 1 + -4.5x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -4.5x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -4.5x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4.5x + x2 = 0 + -1 -4.5x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -4.5x + x2 = -1 The x term is -4.5x. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5x + 5.0625 + x2 = -1 + 5.0625 Reorder the terms: 5.0625 + -4.5x + x2 = -1 + 5.0625 Combine like terms: -1 + 5.0625 = 4.0625 5.0625 + -4.5x + x2 = 4.0625 Factor a perfect square on the left side: (x + -2.25)(x + -2.25) = 4.0625 Calculate the square root of the right side: 2.015564437 Break this problem into two subproblems by setting (x + -2.25) equal to 2.015564437 and -2.015564437.Subproblem 1
x + -2.25 = 2.015564437 Simplifying x + -2.25 = 2.015564437 Reorder the terms: -2.25 + x = 2.015564437 Solving -2.25 + x = 2.015564437 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = 2.015564437 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = 2.015564437 + 2.25 x = 2.015564437 + 2.25 Combine like terms: 2.015564437 + 2.25 = 4.265564437 x = 4.265564437 Simplifying x = 4.265564437Subproblem 2
x + -2.25 = -2.015564437 Simplifying x + -2.25 = -2.015564437 Reorder the terms: -2.25 + x = -2.015564437 Solving -2.25 + x = -2.015564437 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = -2.015564437 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = -2.015564437 + 2.25 x = -2.015564437 + 2.25 Combine like terms: -2.015564437 + 2.25 = 0.234435563 x = 0.234435563 Simplifying x = 0.234435563Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.265564437, 0.234435563}
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