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Simplifying 39 = 3(-10t + -3) * 6t Reorder the terms: 39 = 3(-3 + -10t) * 6t Reorder the terms for easier multiplication: 39 = 3 * 6t(-3 + -10t) Multiply 3 * 6 39 = 18t(-3 + -10t) 39 = (-3 * 18t + -10t * 18t) 39 = (-54t + -180t2) Solving 39 = -54t + -180t2 Solving for variable 't'. Reorder the terms: 39 + 54t + 180t2 = -54t + 54t + -180t2 + 180t2 Combine like terms: -54t + 54t = 0 39 + 54t + 180t2 = 0 + -180t2 + 180t2 39 + 54t + 180t2 = -180t2 + 180t2 Combine like terms: -180t2 + 180t2 = 0 39 + 54t + 180t2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(13 + 18t + 60t2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(13 + 18t + 60t2)' equal to zero and attempt to solve: Simplifying 13 + 18t + 60t2 = 0 Solving 13 + 18t + 60t2 = 0 Begin completing the square. Divide all terms by 60 the coefficient of the squared term: Divide each side by '60'. 0.2166666667 + 0.3t + t2 = 0.0 Move the constant term to the right: Add '-0.2166666667' to each side of the equation. 0.2166666667 + 0.3t + -0.2166666667 + t2 = 0.0 + -0.2166666667 Reorder the terms: 0.2166666667 + -0.2166666667 + 0.3t + t2 = 0.0 + -0.2166666667 Combine like terms: 0.2166666667 + -0.2166666667 = 0.0000000000 0.0000000000 + 0.3t + t2 = 0.0 + -0.2166666667 0.3t + t2 = 0.0 + -0.2166666667 Combine like terms: 0.0 + -0.2166666667 = -0.2166666667 0.3t + t2 = -0.2166666667 The t term is 0.3t. Take half its coefficient (0.15). Square it (0.0225) and add it to both sides. Add '0.0225' to each side of the equation. 0.3t + 0.0225 + t2 = -0.2166666667 + 0.0225 Reorder the terms: 0.0225 + 0.3t + t2 = -0.2166666667 + 0.0225 Combine like terms: -0.2166666667 + 0.0225 = -0.1941666667 0.0225 + 0.3t + t2 = -0.1941666667 Factor a perfect square on the left side: (t + 0.15)(t + 0.15) = -0.1941666667 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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