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Simplifying 16t2 + -115t + -3 = 0 Reorder the terms: -3 + -115t + 16t2 = 0 Solving -3 + -115t + 16t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.1875 + -7.1875t + t2 = 0 Move the constant term to the right: Add '0.1875' to each side of the equation. -0.1875 + -7.1875t + 0.1875 + t2 = 0 + 0.1875 Reorder the terms: -0.1875 + 0.1875 + -7.1875t + t2 = 0 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + -7.1875t + t2 = 0 + 0.1875 -7.1875t + t2 = 0 + 0.1875 Combine like terms: 0 + 0.1875 = 0.1875 -7.1875t + t2 = 0.1875 The t term is -7.1875t. Take half its coefficient (-3.59375). Square it (12.91503906) and add it to both sides. Add '12.91503906' to each side of the equation. -7.1875t + 12.91503906 + t2 = 0.1875 + 12.91503906 Reorder the terms: 12.91503906 + -7.1875t + t2 = 0.1875 + 12.91503906 Combine like terms: 0.1875 + 12.91503906 = 13.10253906 12.91503906 + -7.1875t + t2 = 13.10253906 Factor a perfect square on the left side: (t + -3.59375)(t + -3.59375) = 13.10253906 Calculate the square root of the right side: 3.619742955 Break this problem into two subproblems by setting (t + -3.59375) equal to 3.619742955 and -3.619742955.Subproblem 1
t + -3.59375 = 3.619742955 Simplifying t + -3.59375 = 3.619742955 Reorder the terms: -3.59375 + t = 3.619742955 Solving -3.59375 + t = 3.619742955 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.59375' to each side of the equation. -3.59375 + 3.59375 + t = 3.619742955 + 3.59375 Combine like terms: -3.59375 + 3.59375 = 0.00000 0.00000 + t = 3.619742955 + 3.59375 t = 3.619742955 + 3.59375 Combine like terms: 3.619742955 + 3.59375 = 7.213492955 t = 7.213492955 Simplifying t = 7.213492955Subproblem 2
t + -3.59375 = -3.619742955 Simplifying t + -3.59375 = -3.619742955 Reorder the terms: -3.59375 + t = -3.619742955 Solving -3.59375 + t = -3.619742955 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.59375' to each side of the equation. -3.59375 + 3.59375 + t = -3.619742955 + 3.59375 Combine like terms: -3.59375 + 3.59375 = 0.00000 0.00000 + t = -3.619742955 + 3.59375 t = -3.619742955 + 3.59375 Combine like terms: -3.619742955 + 3.59375 = -0.025992955 t = -0.025992955 Simplifying t = -0.025992955Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.213492955, -0.025992955}
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