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Simplifying x2 + 2x2 + -5x2 + 3x + -4x + 2x + 5 + -1 + 4 = 0 Reorder the terms: 5 + -1 + 4 + 3x + -4x + 2x + x2 + 2x2 + -5x2 = 0 Combine like terms: 5 + -1 = 4 4 + 4 + 3x + -4x + 2x + x2 + 2x2 + -5x2 = 0 Combine like terms: 4 + 4 = 8 8 + 3x + -4x + 2x + x2 + 2x2 + -5x2 = 0 Combine like terms: 3x + -4x = -1x 8 + -1x + 2x + x2 + 2x2 + -5x2 = 0 Combine like terms: -1x + 2x = 1x 8 + 1x + x2 + 2x2 + -5x2 = 0 Combine like terms: x2 + 2x2 = 3x2 8 + 1x + 3x2 + -5x2 = 0 Combine like terms: 3x2 + -5x2 = -2x2 8 + 1x + -2x2 = 0 Solving 8 + 1x + -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'. -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 = 2.265564437 x = 2.265564437 Simplifying x = 2.265564437Subproblem 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 = -1.765564437 x = -1.765564437 Simplifying x = -1.765564437Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.265564437, -1.765564437}
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