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Simplifying -69.8 = -4.905t2 + 1.35t Reorder the terms: -69.8 = 1.35t + -4.905t2 Solving -69.8 = 1.35t + -4.905t2 Solving for variable 't'. Reorder the terms: -69.8 + -1.35t + 4.905t2 = 1.35t + -1.35t + -4.905t2 + 4.905t2 Combine like terms: 1.35t + -1.35t = 0.00 -69.8 + -1.35t + 4.905t2 = 0.00 + -4.905t2 + 4.905t2 -69.8 + -1.35t + 4.905t2 = -4.905t2 + 4.905t2 Combine like terms: -4.905t2 + 4.905t2 = 0.000 -69.8 + -1.35t + 4.905t2 = 0.000 Begin completing the square. Divide all terms by 4.905 the coefficient of the squared term: Divide each side by '4.905'. -14.23037717 + -0.2752293578t + t2 = 0 Move the constant term to the right: Add '14.23037717' to each side of the equation. -14.23037717 + -0.2752293578t + 14.23037717 + t2 = 0 + 14.23037717 Reorder the terms: -14.23037717 + 14.23037717 + -0.2752293578t + t2 = 0 + 14.23037717 Combine like terms: -14.23037717 + 14.23037717 = 0.00000000 0.00000000 + -0.2752293578t + t2 = 0 + 14.23037717 -0.2752293578t + t2 = 0 + 14.23037717 Combine like terms: 0 + 14.23037717 = 14.23037717 -0.2752293578t + t2 = 14.23037717 The t term is -0.2752293578t. Take half its coefficient (-0.1376146789). Square it (0.01893779985) and add it to both sides. Add '0.01893779985' to each side of the equation. -0.2752293578t + 0.01893779985 + t2 = 14.23037717 + 0.01893779985 Reorder the terms: 0.01893779985 + -0.2752293578t + t2 = 14.23037717 + 0.01893779985 Combine like terms: 14.23037717 + 0.01893779985 = 14.24931496985 0.01893779985 + -0.2752293578t + t2 = 14.24931496985 Factor a perfect square on the left side: (t + -0.1376146789)(t + -0.1376146789) = 14.24931496985 Calculate the square root of the right side: 3.774826482 Break this problem into two subproblems by setting (t + -0.1376146789) equal to 3.774826482 and -3.774826482.Subproblem 1
t + -0.1376146789 = 3.774826482 Simplifying t + -0.1376146789 = 3.774826482 Reorder the terms: -0.1376146789 + t = 3.774826482 Solving -0.1376146789 + t = 3.774826482 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.1376146789' to each side of the equation. -0.1376146789 + 0.1376146789 + t = 3.774826482 + 0.1376146789 Combine like terms: -0.1376146789 + 0.1376146789 = 0.0000000000 0.0000000000 + t = 3.774826482 + 0.1376146789 t = 3.774826482 + 0.1376146789 Combine like terms: 3.774826482 + 0.1376146789 = 3.9124411609 t = 3.9124411609 Simplifying t = 3.9124411609Subproblem 2
t + -0.1376146789 = -3.774826482 Simplifying t + -0.1376146789 = -3.774826482 Reorder the terms: -0.1376146789 + t = -3.774826482 Solving -0.1376146789 + t = -3.774826482 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.1376146789' to each side of the equation. -0.1376146789 + 0.1376146789 + t = -3.774826482 + 0.1376146789 Combine like terms: -0.1376146789 + 0.1376146789 = 0.0000000000 0.0000000000 + t = -3.774826482 + 0.1376146789 t = -3.774826482 + 0.1376146789 Combine like terms: -3.774826482 + 0.1376146789 = -3.6372118031 t = -3.6372118031 Simplifying t = -3.6372118031Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.9124411609, -3.6372118031}
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