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Simplifying 2x2 + 4x + -3 = 5 + -2x + -0.5x2 Reorder the terms: -3 + 4x + 2x2 = 5 + -2x + -0.5x2 Solving -3 + 4x + 2x2 = 5 + -2x + -0.5x2 Solving for variable 'x'. Reorder the terms: -3 + -5 + 4x + 2x + 2x2 + 0.5x2 = 5 + -2x + -0.5x2 + -5 + 2x + 0.5x2 Combine like terms: -3 + -5 = -8 -8 + 4x + 2x + 2x2 + 0.5x2 = 5 + -2x + -0.5x2 + -5 + 2x + 0.5x2 Combine like terms: 4x + 2x = 6x -8 + 6x + 2x2 + 0.5x2 = 5 + -2x + -0.5x2 + -5 + 2x + 0.5x2 Combine like terms: 2x2 + 0.5x2 = 2.5x2 -8 + 6x + 2.5x2 = 5 + -2x + -0.5x2 + -5 + 2x + 0.5x2 Reorder the terms: -8 + 6x + 2.5x2 = 5 + -5 + -2x + 2x + -0.5x2 + 0.5x2 Combine like terms: 5 + -5 = 0 -8 + 6x + 2.5x2 = 0 + -2x + 2x + -0.5x2 + 0.5x2 -8 + 6x + 2.5x2 = -2x + 2x + -0.5x2 + 0.5x2 Combine like terms: -2x + 2x = 0 -8 + 6x + 2.5x2 = 0 + -0.5x2 + 0.5x2 -8 + 6x + 2.5x2 = -0.5x2 + 0.5x2 Combine like terms: -0.5x2 + 0.5x2 = 0.0 -8 + 6x + 2.5x2 = 0.0 Begin completing the square. Divide all terms by 2.5 the coefficient of the squared term: Divide each side by '2.5'. -3.2 + 2.4x + x2 = 0 Move the constant term to the right: Add '3.2' to each side of the equation. -3.2 + 2.4x + 3.2 + x2 = 0 + 3.2 Reorder the terms: -3.2 + 3.2 + 2.4x + x2 = 0 + 3.2 Combine like terms: -3.2 + 3.2 = 0.0 0.0 + 2.4x + x2 = 0 + 3.2 2.4x + x2 = 0 + 3.2 Combine like terms: 0 + 3.2 = 3.2 2.4x + x2 = 3.2 The x term is 2.4x. Take half its coefficient (1.2). Square it (1.44) and add it to both sides. Add '1.44' to each side of the equation. 2.4x + 1.44 + x2 = 3.2 + 1.44 Reorder the terms: 1.44 + 2.4x + x2 = 3.2 + 1.44 Combine like terms: 3.2 + 1.44 = 4.64 1.44 + 2.4x + x2 = 4.64 Factor a perfect square on the left side: (x + 1.2)(x + 1.2) = 4.64 Calculate the square root of the right side: 2.154065923 Break this problem into two subproblems by setting (x + 1.2) equal to 2.154065923 and -2.154065923.Subproblem 1
x + 1.2 = 2.154065923 Simplifying x + 1.2 = 2.154065923 Reorder the terms: 1.2 + x = 2.154065923 Solving 1.2 + x = 2.154065923 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.2' to each side of the equation. 1.2 + -1.2 + x = 2.154065923 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + x = 2.154065923 + -1.2 x = 2.154065923 + -1.2 Combine like terms: 2.154065923 + -1.2 = 0.954065923 x = 0.954065923 Simplifying x = 0.954065923Subproblem 2
x + 1.2 = -2.154065923 Simplifying x + 1.2 = -2.154065923 Reorder the terms: 1.2 + x = -2.154065923 Solving 1.2 + x = -2.154065923 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.2' to each side of the equation. 1.2 + -1.2 + x = -2.154065923 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + x = -2.154065923 + -1.2 x = -2.154065923 + -1.2 Combine like terms: -2.154065923 + -1.2 = -3.354065923 x = -3.354065923 Simplifying x = -3.354065923Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.954065923, -3.354065923}
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