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Simplifying 16t2 + 58t + 192 = 0 Reorder the terms: 192 + 58t + 16t2 = 0 Solving 192 + 58t + 16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(96 + 29t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(96 + 29t + 8t2)' equal to zero and attempt to solve: Simplifying 96 + 29t + 8t2 = 0 Solving 96 + 29t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 12 + 3.625t + t2 = 0 Move the constant term to the right: Add '-12' to each side of the equation. 12 + 3.625t + -12 + t2 = 0 + -12 Reorder the terms: 12 + -12 + 3.625t + t2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + 3.625t + t2 = 0 + -12 3.625t + t2 = 0 + -12 Combine like terms: 0 + -12 = -12 3.625t + t2 = -12 The t term is 3.625t. Take half its coefficient (1.8125). Square it (3.28515625) and add it to both sides. Add '3.28515625' to each side of the equation. 3.625t + 3.28515625 + t2 = -12 + 3.28515625 Reorder the terms: 3.28515625 + 3.625t + t2 = -12 + 3.28515625 Combine like terms: -12 + 3.28515625 = -8.71484375 3.28515625 + 3.625t + t2 = -8.71484375 Factor a perfect square on the left side: (t + 1.8125)(t + 1.8125) = -8.71484375 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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