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Simplifying (0.5x2 + 4.25x + -0.9) + -0.5(x2 + 7x + -3) = 0 Reorder the terms: (-0.9 + 4.25x + 0.5x2) + -0.5(x2 + 7x + -3) = 0 Remove parenthesis around (-0.9 + 4.25x + 0.5x2) -0.9 + 4.25x + 0.5x2 + -0.5(x2 + 7x + -3) = 0 Reorder the terms: -0.9 + 4.25x + 0.5x2 + -0.5(-3 + 7x + x2) = 0 -0.9 + 4.25x + 0.5x2 + (-3 * -0.5 + 7x * -0.5 + x2 * -0.5) = 0 -0.9 + 4.25x + 0.5x2 + (1.5 + -3.5x + -0.5x2) = 0 Reorder the terms: -0.9 + 1.5 + 4.25x + -3.5x + 0.5x2 + -0.5x2 = 0 Combine like terms: -0.9 + 1.5 = 0.6 0.6 + 4.25x + -3.5x + 0.5x2 + -0.5x2 = 0 Combine like terms: 4.25x + -3.5x = 0.75x 0.6 + 0.75x + 0.5x2 + -0.5x2 = 0 Combine like terms: 0.5x2 + -0.5x2 = 0.0 0.6 + 0.75x + 0.0 = 0 0.6 + 0.75x = 0 Solving 0.6 + 0.75x = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + 0.75x = 0 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + 0.75x = 0 + -0.6 0.75x = 0 + -0.6 Combine like terms: 0 + -0.6 = -0.6 0.75x = -0.6 Divide each side by '0.75'. x = -0.8 Simplifying x = -0.8
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