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Simplifying (2x5 + 5x4 + 25X3 + 30x2 + 45x + 65) = 0 Reorder the terms: (65 + 25X3 + 45x + 30x2 + 5x4 + 2x5) = 0 Remove parenthesis around (65 + 25X3 + 45x + 30x2 + 5x4 + 2x5) 65 + 25X3 + 45x + 30x2 + 5x4 + 2x5 = 0 Solving 65 + 25X3 + 45x + 30x2 + 5x4 + 2x5 = 0 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-65' to each side of the equation. 65 + 25X3 + 45x + 30x2 + 5x4 + -65 + 2x5 = 0 + -65 Reorder the terms: 65 + -65 + 25X3 + 45x + 30x2 + 5x4 + 2x5 = 0 + -65 Combine like terms: 65 + -65 = 0 0 + 25X3 + 45x + 30x2 + 5x4 + 2x5 = 0 + -65 25X3 + 45x + 30x2 + 5x4 + 2x5 = 0 + -65 Combine like terms: 0 + -65 = -65 25X3 + 45x + 30x2 + 5x4 + 2x5 = -65 Add '-45x' to each side of the equation. 25X3 + 45x + 30x2 + 5x4 + -45x + 2x5 = -65 + -45x Reorder the terms: 25X3 + 45x + -45x + 30x2 + 5x4 + 2x5 = -65 + -45x Combine like terms: 45x + -45x = 0 25X3 + 0 + 30x2 + 5x4 + 2x5 = -65 + -45x 25X3 + 30x2 + 5x4 + 2x5 = -65 + -45x Add '-30x2' to each side of the equation. 25X3 + 30x2 + 5x4 + -30x2 + 2x5 = -65 + -45x + -30x2 Reorder the terms: 25X3 + 30x2 + -30x2 + 5x4 + 2x5 = -65 + -45x + -30x2 Combine like terms: 30x2 + -30x2 = 0 25X3 + 0 + 5x4 + 2x5 = -65 + -45x + -30x2 25X3 + 5x4 + 2x5 = -65 + -45x + -30x2 Add '-5x4' to each side of the equation. 25X3 + 5x4 + -5x4 + 2x5 = -65 + -45x + -30x2 + -5x4 Combine like terms: 5x4 + -5x4 = 0 25X3 + 0 + 2x5 = -65 + -45x + -30x2 + -5x4 25X3 + 2x5 = -65 + -45x + -30x2 + -5x4 Add '-2x5' to each side of the equation. 25X3 + 2x5 + -2x5 = -65 + -45x + -30x2 + -5x4 + -2x5 Combine like terms: 2x5 + -2x5 = 0 25X3 + 0 = -65 + -45x + -30x2 + -5x4 + -2x5 25X3 = -65 + -45x + -30x2 + -5x4 + -2x5 Divide each side by '25'. X3 = -2.6 + -1.8x + -1.2x2 + -0.2x4 + -0.08x5 Simplifying X3 = -2.6 + -1.8x + -1.2x2 + -0.2x4 + -0.08x5 Reorder the terms: 2.6 + X3 + 1.8x + 1.2x2 + 0.2x4 + 0.08x5 = -2.6 + -1.8x + -1.2x2 + -0.2x4 + -0.08x5 + 2.6 + 1.8x + 1.2x2 + 0.2x4 + 0.08x5 Reorder the terms: 2.6 + X3 + 1.8x + 1.2x2 + 0.2x4 + 0.08x5 = -2.6 + 2.6 + -1.8x + 1.8x + -1.2x2 + 1.2x2 + -0.2x4 + 0.2x4 + -0.08x5 + 0.08x5 Combine like terms: -2.6 + 2.6 = 0.0 2.6 + X3 + 1.8x + 1.2x2 + 0.2x4 + 0.08x5 = 0.0 + -1.8x + 1.8x + -1.2x2 + 1.2x2 + -0.2x4 + 0.2x4 + -0.08x5 + 0.08x5 2.6 + X3 + 1.8x + 1.2x2 + 0.2x4 + 0.08x5 = -1.8x + 1.8x + -1.2x2 + 1.2x2 + -0.2x4 + 0.2x4 + -0.08x5 + 0.08x5 Combine like terms: -1.8x + 1.8x = 0.0 2.6 + X3 + 1.8x + 1.2x2 + 0.2x4 + 0.08x5 = 0.0 + -1.2x2 + 1.2x2 + -0.2x4 + 0.2x4 + -0.08x5 + 0.08x5 2.6 + X3 + 1.8x + 1.2x2 + 0.2x4 + 0.08x5 = -1.2x2 + 1.2x2 + -0.2x4 + 0.2x4 + -0.08x5 + 0.08x5 Combine like terms: -1.2x2 + 1.2x2 = 0.0 2.6 + X3 + 1.8x + 1.2x2 + 0.2x4 + 0.08x5 = 0.0 + -0.2x4 + 0.2x4 + -0.08x5 + 0.08x5 2.6 + X3 + 1.8x + 1.2x2 + 0.2x4 + 0.08x5 = -0.2x4 + 0.2x4 + -0.08x5 + 0.08x5 Combine like terms: -0.2x4 + 0.2x4 = 0.0 2.6 + X3 + 1.8x + 1.2x2 + 0.2x4 + 0.08x5 = 0.0 + -0.08x5 + 0.08x5 2.6 + X3 + 1.8x + 1.2x2 + 0.2x4 + 0.08x5 = -0.08x5 + 0.08x5 Combine like terms: -0.08x5 + 0.08x5 = 0.00 2.6 + X3 + 1.8x + 1.2x2 + 0.2x4 + 0.08x5 = 0.00 The solution to this equation could not be determined.
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