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Simplifying 0 = -16t2 + 112t + 3 Reorder the terms: 0 = 3 + 112t + -16t2 Solving 0 = 3 + 112t + -16t2 Solving for variable 't'. Combine like terms: 0 + -3 = -3 -3 + -112t + 16t2 = 3 + 112t + -16t2 + -3 + -112t + 16t2 Reorder the terms: -3 + -112t + 16t2 = 3 + -3 + 112t + -112t + -16t2 + 16t2 Combine like terms: 3 + -3 = 0 -3 + -112t + 16t2 = 0 + 112t + -112t + -16t2 + 16t2 -3 + -112t + 16t2 = 112t + -112t + -16t2 + 16t2 Combine like terms: 112t + -112t = 0 -3 + -112t + 16t2 = 0 + -16t2 + 16t2 -3 + -112t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -3 + -112t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.1875 + -7t + t2 = 0 Move the constant term to the right: Add '0.1875' to each side of the equation. -0.1875 + -7t + 0.1875 + t2 = 0 + 0.1875 Reorder the terms: -0.1875 + 0.1875 + -7t + t2 = 0 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + -7t + t2 = 0 + 0.1875 -7t + t2 = 0 + 0.1875 Combine like terms: 0 + 0.1875 = 0.1875 -7t + t2 = 0.1875 The t term is -7t. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7t + 12.25 + t2 = 0.1875 + 12.25 Reorder the terms: 12.25 + -7t + t2 = 0.1875 + 12.25 Combine like terms: 0.1875 + 12.25 = 12.4375 12.25 + -7t + t2 = 12.4375 Factor a perfect square on the left side: (t + -3.5)(t + -3.5) = 12.4375 Calculate the square root of the right side: 3.526683995 Break this problem into two subproblems by setting (t + -3.5) equal to 3.526683995 and -3.526683995.Subproblem 1
t + -3.5 = 3.526683995 Simplifying t + -3.5 = 3.526683995 Reorder the terms: -3.5 + t = 3.526683995 Solving -3.5 + t = 3.526683995 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + t = 3.526683995 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + t = 3.526683995 + 3.5 t = 3.526683995 + 3.5 Combine like terms: 3.526683995 + 3.5 = 7.026683995 t = 7.026683995 Simplifying t = 7.026683995Subproblem 2
t + -3.5 = -3.526683995 Simplifying t + -3.5 = -3.526683995 Reorder the terms: -3.5 + t = -3.526683995 Solving -3.5 + t = -3.526683995 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + t = -3.526683995 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + t = -3.526683995 + 3.5 t = -3.526683995 + 3.5 Combine like terms: -3.526683995 + 3.5 = -0.026683995 t = -0.026683995 Simplifying t = -0.026683995Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.026683995, -0.026683995}
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