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Simplifying 3(x + -1) + -4x = 5 + -2x(x + 1) Reorder the terms: 3(-1 + x) + -4x = 5 + -2x(x + 1) (-1 * 3 + x * 3) + -4x = 5 + -2x(x + 1) (-3 + 3x) + -4x = 5 + -2x(x + 1) Combine like terms: 3x + -4x = -1x -3 + -1x = 5 + -2x(x + 1) Reorder the terms: -3 + -1x = 5 + -2x(1 + x) -3 + -1x = 5 + (1 * -2x + x * -2x) -3 + -1x = 5 + (-2x + -2x2) Solving -3 + -1x = 5 + -2x + -2x2 Solving for variable 'x'. Reorder the terms: -3 + -5 + -1x + 2x + 2x2 = 5 + -2x + -2x2 + -5 + 2x + 2x2 Combine like terms: -3 + -5 = -8 -8 + -1x + 2x + 2x2 = 5 + -2x + -2x2 + -5 + 2x + 2x2 Combine like terms: -1x + 2x = 1x -8 + 1x + 2x2 = 5 + -2x + -2x2 + -5 + 2x + 2x2 Reorder the terms: -8 + 1x + 2x2 = 5 + -5 + -2x + 2x + -2x2 + 2x2 Combine like terms: 5 + -5 = 0 -8 + 1x + 2x2 = 0 + -2x + 2x + -2x2 + 2x2 -8 + 1x + 2x2 = -2x + 2x + -2x2 + 2x2 Combine like terms: -2x + 2x = 0 -8 + 1x + 2x2 = 0 + -2x2 + 2x2 -8 + 1x + 2x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 -8 + 1x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -4 + 0.5x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + 0.5x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + 0.5x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 0.5x + x2 = 0 + 4 0.5x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 0.5x + x2 = 4 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = 4 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 4 + 0.0625 Combine like terms: 4 + 0.0625 = 4.0625 0.0625 + 0.5x + x2 = 4.0625 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 4.0625 Calculate the square root of the right side: 2.015564437 Break this problem into two subproblems by setting (x + 0.25) equal to 2.015564437 and -2.015564437.Subproblem 1
x + 0.25 = 2.015564437 Simplifying x + 0.25 = 2.015564437 Reorder the terms: 0.25 + x = 2.015564437 Solving 0.25 + x = 2.015564437 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 2.015564437 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 2.015564437 + -0.25 x = 2.015564437 + -0.25 Combine like terms: 2.015564437 + -0.25 = 1.765564437 x = 1.765564437 Simplifying x = 1.765564437Subproblem 2
x + 0.25 = -2.015564437 Simplifying x + 0.25 = -2.015564437 Reorder the terms: 0.25 + x = -2.015564437 Solving 0.25 + x = -2.015564437 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -2.015564437 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -2.015564437 + -0.25 x = -2.015564437 + -0.25 Combine like terms: -2.015564437 + -0.25 = -2.265564437 x = -2.265564437 Simplifying x = -2.265564437Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.765564437, -2.265564437}
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