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Simplifying x2 + -5x + 42 = x2 + 6x + -7.5 Reorder the terms: 42 + -5x + x2 = x2 + 6x + -7.5 Reorder the terms: 42 + -5x + x2 = -7.5 + 6x + x2 Add '-1x2' to each side of the equation. 42 + -5x + x2 + -1x2 = -7.5 + 6x + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 42 + -5x + 0 = -7.5 + 6x + x2 + -1x2 42 + -5x = -7.5 + 6x + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 42 + -5x = -7.5 + 6x + 0 42 + -5x = -7.5 + 6x Solving 42 + -5x = -7.5 + 6x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6x' to each side of the equation. 42 + -5x + -6x = -7.5 + 6x + -6x Combine like terms: -5x + -6x = -11x 42 + -11x = -7.5 + 6x + -6x Combine like terms: 6x + -6x = 0 42 + -11x = -7.5 + 0 42 + -11x = -7.5 Add '-42' to each side of the equation. 42 + -42 + -11x = -7.5 + -42 Combine like terms: 42 + -42 = 0 0 + -11x = -7.5 + -42 -11x = -7.5 + -42 Combine like terms: -7.5 + -42 = -49.5 -11x = -49.5 Divide each side by '-11'. x = 4.5 Simplifying x = 4.5
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