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Simplifying 0 = 16t2 + 63t + 125 Reorder the terms: 0 = 125 + 63t + 16t2 Solving 0 = 125 + 63t + 16t2 Solving for variable 't'. Combine like terms: 0 + -125 = -125 -125 + -63t + -16t2 = 125 + 63t + 16t2 + -125 + -63t + -16t2 Reorder the terms: -125 + -63t + -16t2 = 125 + -125 + 63t + -63t + 16t2 + -16t2 Combine like terms: 125 + -125 = 0 -125 + -63t + -16t2 = 0 + 63t + -63t + 16t2 + -16t2 -125 + -63t + -16t2 = 63t + -63t + 16t2 + -16t2 Combine like terms: 63t + -63t = 0 -125 + -63t + -16t2 = 0 + 16t2 + -16t2 -125 + -63t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 -125 + -63t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(125 + 63t + 16t2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(125 + 63t + 16t2)' equal to zero and attempt to solve: Simplifying 125 + 63t + 16t2 = 0 Solving 125 + 63t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 7.8125 + 3.9375t + t2 = 0 Move the constant term to the right: Add '-7.8125' to each side of the equation. 7.8125 + 3.9375t + -7.8125 + t2 = 0 + -7.8125 Reorder the terms: 7.8125 + -7.8125 + 3.9375t + t2 = 0 + -7.8125 Combine like terms: 7.8125 + -7.8125 = 0.0000 0.0000 + 3.9375t + t2 = 0 + -7.8125 3.9375t + t2 = 0 + -7.8125 Combine like terms: 0 + -7.8125 = -7.8125 3.9375t + t2 = -7.8125 The t term is 3.9375t. Take half its coefficient (1.96875). Square it (3.875976563) and add it to both sides. Add '3.875976563' to each side of the equation. 3.9375t + 3.875976563 + t2 = -7.8125 + 3.875976563 Reorder the terms: 3.875976563 + 3.9375t + t2 = -7.8125 + 3.875976563 Combine like terms: -7.8125 + 3.875976563 = -3.936523437 3.875976563 + 3.9375t + t2 = -3.936523437 Factor a perfect square on the left side: (t + 1.96875)(t + 1.96875) = -3.936523437 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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