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Simplifying 1500 = (x + 24 + 25)(x + 24) + -1(x + 24)(x) Reorder the terms: 1500 = (24 + 25 + x)(x + 24) + -1(x + 24)(x) Combine like terms: 24 + 25 = 49 1500 = (49 + x)(x + 24) + -1(x + 24)(x) Reorder the terms: 1500 = (49 + x)(24 + x) + -1(x + 24)(x) Multiply (49 + x) * (24 + x) 1500 = (49(24 + x) + x(24 + x)) + -1(x + 24)(x) 1500 = ((24 * 49 + x * 49) + x(24 + x)) + -1(x + 24)(x) 1500 = ((1176 + 49x) + x(24 + x)) + -1(x + 24)(x) 1500 = (1176 + 49x + (24 * x + x * x)) + -1(x + 24)(x) 1500 = (1176 + 49x + (24x + x2)) + -1(x + 24)(x) Combine like terms: 49x + 24x = 73x 1500 = (1176 + 73x + x2) + -1(x + 24)(x) Reorder the terms: 1500 = 1176 + 73x + x2 + -1(24 + x)(x) Reorder the terms for easier multiplication: 1500 = 1176 + 73x + x2 + -1x(24 + x) 1500 = 1176 + 73x + x2 + (24 * -1x + x * -1x) 1500 = 1176 + 73x + x2 + (-24x + -1x2) Reorder the terms: 1500 = 1176 + 73x + -24x + x2 + -1x2 Combine like terms: 73x + -24x = 49x 1500 = 1176 + 49x + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 1500 = 1176 + 49x + 0 1500 = 1176 + 49x Solving 1500 = 1176 + 49x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-49x' to each side of the equation. 1500 + -49x = 1176 + 49x + -49x Combine like terms: 49x + -49x = 0 1500 + -49x = 1176 + 0 1500 + -49x = 1176 Add '-1500' to each side of the equation. 1500 + -1500 + -49x = 1176 + -1500 Combine like terms: 1500 + -1500 = 0 0 + -49x = 1176 + -1500 -49x = 1176 + -1500 Combine like terms: 1176 + -1500 = -324 -49x = -324 Divide each side by '-49'. x = 6.612244898 Simplifying x = 6.612244898
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