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Simplifying t = 16t2 + 32t + 128 Reorder the terms: t = 128 + 32t + 16t2 Solving t = 128 + 32t + 16t2 Solving for variable 't'. Reorder the terms: -128 + t + -32t + -16t2 = 128 + 32t + 16t2 + -128 + -32t + -16t2 Combine like terms: t + -32t = -31t -128 + -31t + -16t2 = 128 + 32t + 16t2 + -128 + -32t + -16t2 Reorder the terms: -128 + -31t + -16t2 = 128 + -128 + 32t + -32t + 16t2 + -16t2 Combine like terms: 128 + -128 = 0 -128 + -31t + -16t2 = 0 + 32t + -32t + 16t2 + -16t2 -128 + -31t + -16t2 = 32t + -32t + 16t2 + -16t2 Combine like terms: 32t + -32t = 0 -128 + -31t + -16t2 = 0 + 16t2 + -16t2 -128 + -31t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 -128 + -31t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(128 + 31t + 16t2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(128 + 31t + 16t2)' equal to zero and attempt to solve: Simplifying 128 + 31t + 16t2 = 0 Solving 128 + 31t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 8 + 1.9375t + t2 = 0 Move the constant term to the right: Add '-8' to each side of the equation. 8 + 1.9375t + -8 + t2 = 0 + -8 Reorder the terms: 8 + -8 + 1.9375t + t2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 1.9375t + t2 = 0 + -8 1.9375t + t2 = 0 + -8 Combine like terms: 0 + -8 = -8 1.9375t + t2 = -8 The t term is 1.9375t. Take half its coefficient (0.96875). Square it (0.9384765625) and add it to both sides. Add '0.9384765625' to each side of the equation. 1.9375t + 0.9384765625 + t2 = -8 + 0.9384765625 Reorder the terms: 0.9384765625 + 1.9375t + t2 = -8 + 0.9384765625 Combine like terms: -8 + 0.9384765625 = -7.0615234375 0.9384765625 + 1.9375t + t2 = -7.0615234375 Factor a perfect square on the left side: (t + 0.96875)(t + 0.96875) = -7.0615234375 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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