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Simplifying 3(0.5x2 + 1) + 4x + -1x2 = 0.5x2 + 0.5x + 5 Reorder the terms: 3(1 + 0.5x2) + 4x + -1x2 = 0.5x2 + 0.5x + 5 (1 * 3 + 0.5x2 * 3) + 4x + -1x2 = 0.5x2 + 0.5x + 5 (3 + 1.5x2) + 4x + -1x2 = 0.5x2 + 0.5x + 5 Reorder the terms: 3 + 4x + 1.5x2 + -1x2 = 0.5x2 + 0.5x + 5 Combine like terms: 1.5x2 + -1x2 = 0.5x2 3 + 4x + 0.5x2 = 0.5x2 + 0.5x + 5 Reorder the terms: 3 + 4x + 0.5x2 = 5 + 0.5x + 0.5x2 Add '-0.5x2' to each side of the equation. 3 + 4x + 0.5x2 + -0.5x2 = 5 + 0.5x + 0.5x2 + -0.5x2 Combine like terms: 0.5x2 + -0.5x2 = 0.0 3 + 4x + 0.0 = 5 + 0.5x + 0.5x2 + -0.5x2 3 + 4x = 5 + 0.5x + 0.5x2 + -0.5x2 Combine like terms: 0.5x2 + -0.5x2 = 0.0 3 + 4x = 5 + 0.5x + 0.0 3 + 4x = 5 + 0.5x Solving 3 + 4x = 5 + 0.5x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5x' to each side of the equation. 3 + 4x + -0.5x = 5 + 0.5x + -0.5x Combine like terms: 4x + -0.5x = 3.5x 3 + 3.5x = 5 + 0.5x + -0.5x Combine like terms: 0.5x + -0.5x = 0.0 3 + 3.5x = 5 + 0.0 3 + 3.5x = 5 Add '-3' to each side of the equation. 3 + -3 + 3.5x = 5 + -3 Combine like terms: 3 + -3 = 0 0 + 3.5x = 5 + -3 3.5x = 5 + -3 Combine like terms: 5 + -3 = 2 3.5x = 2 Divide each side by '3.5'. x = 0.5714285714 Simplifying x = 0.5714285714
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