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Simplifying 5.4t + 14.6 + -10.1t = 0.4(25 + j) Reorder the terms: 14.6 + 5.4t + -10.1t = 0.4(25 + j) Combine like terms: 5.4t + -10.1t = -4.7t 14.6 + -4.7t = 0.4(25 + j) 14.6 + -4.7t = (25 * 0.4 + j * 0.4) 14.6 + -4.7t = (10 + 0.4j) Solving 14.6 + -4.7t = 10 + 0.4j Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-14.6' to each side of the equation. 14.6 + -14.6 + -4.7t = 10 + -14.6 + 0.4j Combine like terms: 14.6 + -14.6 = 0.0 0.0 + -4.7t = 10 + -14.6 + 0.4j -4.7t = 10 + -14.6 + 0.4j Combine like terms: 10 + -14.6 = -4.6 -4.7t = -4.6 + 0.4j Divide each side by '-4.7'. t = 0.9787234043 + -0.08510638298j Simplifying t = 0.9787234043 + -0.08510638298j
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