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Simplifying t = 0.3t2 + 0.6t + 0.5 Reorder the terms: t = 0.5 + 0.6t + 0.3t2 Solving t = 0.5 + 0.6t + 0.3t2 Solving for variable 't'. Reorder the terms: -0.5 + t + -0.6t + -0.3t2 = 0.5 + 0.6t + 0.3t2 + -0.5 + -0.6t + -0.3t2 Combine like terms: t + -0.6t = 0.4t -0.5 + 0.4t + -0.3t2 = 0.5 + 0.6t + 0.3t2 + -0.5 + -0.6t + -0.3t2 Reorder the terms: -0.5 + 0.4t + -0.3t2 = 0.5 + -0.5 + 0.6t + -0.6t + 0.3t2 + -0.3t2 Combine like terms: 0.5 + -0.5 = 0.0 -0.5 + 0.4t + -0.3t2 = 0.0 + 0.6t + -0.6t + 0.3t2 + -0.3t2 -0.5 + 0.4t + -0.3t2 = 0.6t + -0.6t + 0.3t2 + -0.3t2 Combine like terms: 0.6t + -0.6t = 0.0 -0.5 + 0.4t + -0.3t2 = 0.0 + 0.3t2 + -0.3t2 -0.5 + 0.4t + -0.3t2 = 0.3t2 + -0.3t2 Combine like terms: 0.3t2 + -0.3t2 = 0.0 -0.5 + 0.4t + -0.3t2 = 0.0 Begin completing the square. Divide all terms by -0.3 the coefficient of the squared term: Divide each side by '-0.3'. 1.666666667 + -1.333333333t + t2 = 0 Move the constant term to the right: Add '-1.666666667' to each side of the equation. 1.666666667 + -1.333333333t + -1.666666667 + t2 = 0 + -1.666666667 Reorder the terms: 1.666666667 + -1.666666667 + -1.333333333t + t2 = 0 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + -1.333333333t + t2 = 0 + -1.666666667 -1.333333333t + t2 = 0 + -1.666666667 Combine like terms: 0 + -1.666666667 = -1.666666667 -1.333333333t + t2 = -1.666666667 The t term is -1.333333333t. Take half its coefficient (-0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. -1.333333333t + 0.4444444442 + t2 = -1.666666667 + 0.4444444442 Reorder the terms: 0.4444444442 + -1.333333333t + t2 = -1.666666667 + 0.4444444442 Combine like terms: -1.666666667 + 0.4444444442 = -1.2222222228 0.4444444442 + -1.333333333t + t2 = -1.2222222228 Factor a perfect square on the left side: (t + -0.6666666665)(t + -0.6666666665) = -1.2222222228 Can't calculate square root of the right side. The solution to this equation could not be determined.
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