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Simplifying 64t2 + 28t + 1156 = 0 Reorder the terms: 1156 + 28t + 64t2 = 0 Solving 1156 + 28t + 64t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '4'. 4(289 + 7t + 16t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(289 + 7t + 16t2)' equal to zero and attempt to solve: Simplifying 289 + 7t + 16t2 = 0 Solving 289 + 7t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 18.0625 + 0.4375t + t2 = 0 Move the constant term to the right: Add '-18.0625' to each side of the equation. 18.0625 + 0.4375t + -18.0625 + t2 = 0 + -18.0625 Reorder the terms: 18.0625 + -18.0625 + 0.4375t + t2 = 0 + -18.0625 Combine like terms: 18.0625 + -18.0625 = 0.0000 0.0000 + 0.4375t + t2 = 0 + -18.0625 0.4375t + t2 = 0 + -18.0625 Combine like terms: 0 + -18.0625 = -18.0625 0.4375t + t2 = -18.0625 The t term is 0.4375t. Take half its coefficient (0.21875). Square it (0.0478515625) and add it to both sides. Add '0.0478515625' to each side of the equation. 0.4375t + 0.0478515625 + t2 = -18.0625 + 0.0478515625 Reorder the terms: 0.0478515625 + 0.4375t + t2 = -18.0625 + 0.0478515625 Combine like terms: -18.0625 + 0.0478515625 = -18.0146484375 0.0478515625 + 0.4375t + t2 = -18.0146484375 Factor a perfect square on the left side: (t + 0.21875)(t + 0.21875) = -18.0146484375 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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