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Simplifying 6 = -15.9t2 + 110.5t + 3.02 Reorder the terms: 6 = 3.02 + 110.5t + -15.9t2 Solving 6 = 3.02 + 110.5t + -15.9t2 Solving for variable 't'. Combine like terms: 6 + -3.02 = 2.98 2.98 + -110.5t + 15.9t2 = 3.02 + 110.5t + -15.9t2 + -3.02 + -110.5t + 15.9t2 Reorder the terms: 2.98 + -110.5t + 15.9t2 = 3.02 + -3.02 + 110.5t + -110.5t + -15.9t2 + 15.9t2 Combine like terms: 3.02 + -3.02 = 0.00 2.98 + -110.5t + 15.9t2 = 0.00 + 110.5t + -110.5t + -15.9t2 + 15.9t2 2.98 + -110.5t + 15.9t2 = 110.5t + -110.5t + -15.9t2 + 15.9t2 Combine like terms: 110.5t + -110.5t = 0.0 2.98 + -110.5t + 15.9t2 = 0.0 + -15.9t2 + 15.9t2 2.98 + -110.5t + 15.9t2 = -15.9t2 + 15.9t2 Combine like terms: -15.9t2 + 15.9t2 = 0.0 2.98 + -110.5t + 15.9t2 = 0.0 Begin completing the square. Divide all terms by 15.9 the coefficient of the squared term: Divide each side by '15.9'. 0.1874213836 + -6.949685535t + t2 = 0 Move the constant term to the right: Add '-0.1874213836' to each side of the equation. 0.1874213836 + -6.949685535t + -0.1874213836 + t2 = 0 + -0.1874213836 Reorder the terms: 0.1874213836 + -0.1874213836 + -6.949685535t + t2 = 0 + -0.1874213836 Combine like terms: 0.1874213836 + -0.1874213836 = 0.0000000000 0.0000000000 + -6.949685535t + t2 = 0 + -0.1874213836 -6.949685535t + t2 = 0 + -0.1874213836 Combine like terms: 0 + -0.1874213836 = -0.1874213836 -6.949685535t + t2 = -0.1874213836 The t term is -6.949685535t. Take half its coefficient (-3.474842768). Square it (12.07453226) and add it to both sides. Add '12.07453226' to each side of the equation. -6.949685535t + 12.07453226 + t2 = -0.1874213836 + 12.07453226 Reorder the terms: 12.07453226 + -6.949685535t + t2 = -0.1874213836 + 12.07453226 Combine like terms: -0.1874213836 + 12.07453226 = 11.8871108764 12.07453226 + -6.949685535t + t2 = 11.8871108764 Factor a perfect square on the left side: (t + -3.474842768)(t + -3.474842768) = 11.8871108764 Calculate the square root of the right side: 3.447768971 Break this problem into two subproblems by setting (t + -3.474842768) equal to 3.447768971 and -3.447768971.Subproblem 1
t + -3.474842768 = 3.447768971 Simplifying t + -3.474842768 = 3.447768971 Reorder the terms: -3.474842768 + t = 3.447768971 Solving -3.474842768 + t = 3.447768971 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.474842768' to each side of the equation. -3.474842768 + 3.474842768 + t = 3.447768971 + 3.474842768 Combine like terms: -3.474842768 + 3.474842768 = 0.000000000 0.000000000 + t = 3.447768971 + 3.474842768 t = 3.447768971 + 3.474842768 Combine like terms: 3.447768971 + 3.474842768 = 6.922611739 t = 6.922611739 Simplifying t = 6.922611739Subproblem 2
t + -3.474842768 = -3.447768971 Simplifying t + -3.474842768 = -3.447768971 Reorder the terms: -3.474842768 + t = -3.447768971 Solving -3.474842768 + t = -3.447768971 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.474842768' to each side of the equation. -3.474842768 + 3.474842768 + t = -3.447768971 + 3.474842768 Combine like terms: -3.474842768 + 3.474842768 = 0.000000000 0.000000000 + t = -3.447768971 + 3.474842768 t = -3.447768971 + 3.474842768 Combine like terms: -3.447768971 + 3.474842768 = 0.027073797 t = 0.027073797 Simplifying t = 0.027073797Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.922611739, 0.027073797}
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