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Simplifying 446 = 16t2 + -6t + 470 Reorder the terms: 446 = 470 + -6t + 16t2 Solving 446 = 470 + -6t + 16t2 Solving for variable 't'. Combine like terms: 446 + -470 = -24 -24 + 6t + -16t2 = 470 + -6t + 16t2 + -470 + 6t + -16t2 Reorder the terms: -24 + 6t + -16t2 = 470 + -470 + -6t + 6t + 16t2 + -16t2 Combine like terms: 470 + -470 = 0 -24 + 6t + -16t2 = 0 + -6t + 6t + 16t2 + -16t2 -24 + 6t + -16t2 = -6t + 6t + 16t2 + -16t2 Combine like terms: -6t + 6t = 0 -24 + 6t + -16t2 = 0 + 16t2 + -16t2 -24 + 6t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 -24 + 6t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-12 + 3t + -8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-12 + 3t + -8t2)' equal to zero and attempt to solve: Simplifying -12 + 3t + -8t2 = 0 Solving -12 + 3t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. 1.5 + -0.375t + t2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + -0.375t + -1.5 + t2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + -0.375t + t2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + -0.375t + t2 = 0 + -1.5 -0.375t + t2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 -0.375t + t2 = -1.5 The t term is -0.375t. Take half its coefficient (-0.1875). Square it (0.03515625) and add it to both sides. Add '0.03515625' to each side of the equation. -0.375t + 0.03515625 + t2 = -1.5 + 0.03515625 Reorder the terms: 0.03515625 + -0.375t + t2 = -1.5 + 0.03515625 Combine like terms: -1.5 + 0.03515625 = -1.46484375 0.03515625 + -0.375t + t2 = -1.46484375 Factor a perfect square on the left side: (t + -0.1875)(t + -0.1875) = -1.46484375 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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