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Simplifying 182 = 12t + -16t2 Solving 182 = 12t + -16t2 Solving for variable 't'. Reorder the terms: 182 + -12t + 16t2 = 12t + -12t + -16t2 + 16t2 Combine like terms: 12t + -12t = 0 182 + -12t + 16t2 = 0 + -16t2 + 16t2 182 + -12t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 182 + -12t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(91 + -6t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(91 + -6t + 8t2)' equal to zero and attempt to solve: Simplifying 91 + -6t + 8t2 = 0 Solving 91 + -6t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 11.375 + -0.75t + t2 = 0 Move the constant term to the right: Add '-11.375' to each side of the equation. 11.375 + -0.75t + -11.375 + t2 = 0 + -11.375 Reorder the terms: 11.375 + -11.375 + -0.75t + t2 = 0 + -11.375 Combine like terms: 11.375 + -11.375 = 0.000 0.000 + -0.75t + t2 = 0 + -11.375 -0.75t + t2 = 0 + -11.375 Combine like terms: 0 + -11.375 = -11.375 -0.75t + t2 = -11.375 The t term is -0.75t. Take half its coefficient (-0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. -0.75t + 0.140625 + t2 = -11.375 + 0.140625 Reorder the terms: 0.140625 + -0.75t + t2 = -11.375 + 0.140625 Combine like terms: -11.375 + 0.140625 = -11.234375 0.140625 + -0.75t + t2 = -11.234375 Factor a perfect square on the left side: (t + -0.375)(t + -0.375) = -11.234375 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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