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Simplifying 2.2 = -16t2 + 12t + 7.8 Reorder the terms: 2.2 = 7.8 + 12t + -16t2 Solving 2.2 = 7.8 + 12t + -16t2 Solving for variable 't'. Combine like terms: 2.2 + -7.8 = -5.6 -5.6 + -12t + 16t2 = 7.8 + 12t + -16t2 + -7.8 + -12t + 16t2 Reorder the terms: -5.6 + -12t + 16t2 = 7.8 + -7.8 + 12t + -12t + -16t2 + 16t2 Combine like terms: 7.8 + -7.8 = 0.0 -5.6 + -12t + 16t2 = 0.0 + 12t + -12t + -16t2 + 16t2 -5.6 + -12t + 16t2 = 12t + -12t + -16t2 + 16t2 Combine like terms: 12t + -12t = 0 -5.6 + -12t + 16t2 = 0 + -16t2 + 16t2 -5.6 + -12t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -5.6 + -12t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.35 + -0.75t + t2 = 0 Move the constant term to the right: Add '0.35' to each side of the equation. -0.35 + -0.75t + 0.35 + t2 = 0 + 0.35 Reorder the terms: -0.35 + 0.35 + -0.75t + t2 = 0 + 0.35 Combine like terms: -0.35 + 0.35 = 0.00 0.00 + -0.75t + t2 = 0 + 0.35 -0.75t + t2 = 0 + 0.35 Combine like terms: 0 + 0.35 = 0.35 -0.75t + t2 = 0.35 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 = 0.35 + 0.140625 Reorder the terms: 0.140625 + -0.75t + t2 = 0.35 + 0.140625 Combine like terms: 0.35 + 0.140625 = 0.490625 0.140625 + -0.75t + t2 = 0.490625 Factor a perfect square on the left side: (t + -0.375)(t + -0.375) = 0.490625 Calculate the square root of the right side: 0.700446286 Break this problem into two subproblems by setting (t + -0.375) equal to 0.700446286 and -0.700446286.Subproblem 1
t + -0.375 = 0.700446286 Simplifying t + -0.375 = 0.700446286 Reorder the terms: -0.375 + t = 0.700446286 Solving -0.375 + t = 0.700446286 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + t = 0.700446286 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + t = 0.700446286 + 0.375 t = 0.700446286 + 0.375 Combine like terms: 0.700446286 + 0.375 = 1.075446286 t = 1.075446286 Simplifying t = 1.075446286Subproblem 2
t + -0.375 = -0.700446286 Simplifying t + -0.375 = -0.700446286 Reorder the terms: -0.375 + t = -0.700446286 Solving -0.375 + t = -0.700446286 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + t = -0.700446286 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + t = -0.700446286 + 0.375 t = -0.700446286 + 0.375 Combine like terms: -0.700446286 + 0.375 = -0.325446286 t = -0.325446286 Simplifying t = -0.325446286Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.075446286, -0.325446286}
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