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Simplifying -1t = 3t2 + 5 Reorder the terms: -1t = 5 + 3t2 Solving -1t = 5 + 3t2 Solving for variable 't'. Reorder the terms: -5 + -1t + -3t2 = 5 + 3t2 + -5 + -3t2 Reorder the terms: -5 + -1t + -3t2 = 5 + -5 + 3t2 + -3t2 Combine like terms: 5 + -5 = 0 -5 + -1t + -3t2 = 0 + 3t2 + -3t2 -5 + -1t + -3t2 = 3t2 + -3t2 Combine like terms: 3t2 + -3t2 = 0 -5 + -1t + -3t2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(5 + t + 3t2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(5 + t + 3t2)' equal to zero and attempt to solve: Simplifying 5 + t + 3t2 = 0 Solving 5 + t + 3t2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 1.666666667 + 0.3333333333t + t2 = 0 Move the constant term to the right: Add '-1.666666667' to each side of the equation. 1.666666667 + 0.3333333333t + -1.666666667 + t2 = 0 + -1.666666667 Reorder the terms: 1.666666667 + -1.666666667 + 0.3333333333t + t2 = 0 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + 0.3333333333t + t2 = 0 + -1.666666667 0.3333333333t + t2 = 0 + -1.666666667 Combine like terms: 0 + -1.666666667 = -1.666666667 0.3333333333t + t2 = -1.666666667 The t term is t. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.3333333333t + 0.25 + t2 = -1.666666667 + 0.25 Reorder the terms: 0.25 + 0.3333333333t + t2 = -1.666666667 + 0.25 Combine like terms: -1.666666667 + 0.25 = -1.416666667 0.25 + 0.3333333333t + t2 = -1.416666667 Factor a perfect square on the left side: (t + 0.5)(t + 0.5) = -1.416666667 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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