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Simplifying x2 + -3x = 8x + -4x2 + 2 Reorder the terms: -3x + x2 = 8x + -4x2 + 2 Reorder the terms: -3x + x2 = 2 + 8x + -4x2 Solving -3x + x2 = 2 + 8x + -4x2 Solving for variable 'x'. Reorder the terms: -2 + -3x + -8x + x2 + 4x2 = 2 + 8x + -4x2 + -2 + -8x + 4x2 Combine like terms: -3x + -8x = -11x -2 + -11x + x2 + 4x2 = 2 + 8x + -4x2 + -2 + -8x + 4x2 Combine like terms: x2 + 4x2 = 5x2 -2 + -11x + 5x2 = 2 + 8x + -4x2 + -2 + -8x + 4x2 Reorder the terms: -2 + -11x + 5x2 = 2 + -2 + 8x + -8x + -4x2 + 4x2 Combine like terms: 2 + -2 = 0 -2 + -11x + 5x2 = 0 + 8x + -8x + -4x2 + 4x2 -2 + -11x + 5x2 = 8x + -8x + -4x2 + 4x2 Combine like terms: 8x + -8x = 0 -2 + -11x + 5x2 = 0 + -4x2 + 4x2 -2 + -11x + 5x2 = -4x2 + 4x2 Combine like terms: -4x2 + 4x2 = 0 -2 + -11x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.4 + -2.2x + x2 = 0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + -2.2x + 0.4 + x2 = 0 + 0.4 Reorder the terms: -0.4 + 0.4 + -2.2x + x2 = 0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + -2.2x + x2 = 0 + 0.4 -2.2x + x2 = 0 + 0.4 Combine like terms: 0 + 0.4 = 0.4 -2.2x + x2 = 0.4 The x term is -2.2x. Take half its coefficient (-1.1). Square it (1.21) and add it to both sides. Add '1.21' to each side of the equation. -2.2x + 1.21 + x2 = 0.4 + 1.21 Reorder the terms: 1.21 + -2.2x + x2 = 0.4 + 1.21 Combine like terms: 0.4 + 1.21 = 1.61 1.21 + -2.2x + x2 = 1.61 Factor a perfect square on the left side: (x + -1.1)(x + -1.1) = 1.61 Calculate the square root of the right side: 1.268857754 Break this problem into two subproblems by setting (x + -1.1) equal to 1.268857754 and -1.268857754.Subproblem 1
x + -1.1 = 1.268857754 Simplifying x + -1.1 = 1.268857754 Reorder the terms: -1.1 + x = 1.268857754 Solving -1.1 + x = 1.268857754 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.1' to each side of the equation. -1.1 + 1.1 + x = 1.268857754 + 1.1 Combine like terms: -1.1 + 1.1 = 0.0 0.0 + x = 1.268857754 + 1.1 x = 1.268857754 + 1.1 Combine like terms: 1.268857754 + 1.1 = 2.368857754 x = 2.368857754 Simplifying x = 2.368857754Subproblem 2
x + -1.1 = -1.268857754 Simplifying x + -1.1 = -1.268857754 Reorder the terms: -1.1 + x = -1.268857754 Solving -1.1 + x = -1.268857754 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.1' to each side of the equation. -1.1 + 1.1 + x = -1.268857754 + 1.1 Combine like terms: -1.1 + 1.1 = 0.0 0.0 + x = -1.268857754 + 1.1 x = -1.268857754 + 1.1 Combine like terms: -1.268857754 + 1.1 = -0.168857754 x = -0.168857754 Simplifying x = -0.168857754Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.368857754, -0.168857754}
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