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Simplifying -16t2 + -19t + 1200 = 0 Reorder the terms: 1200 + -19t + -16t2 = 0 Solving 1200 + -19t + -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'. -75 + 1.1875t + t2 = 0 Move the constant term to the right: Add '75' to each side of the equation. -75 + 1.1875t + 75 + t2 = 0 + 75 Reorder the terms: -75 + 75 + 1.1875t + t2 = 0 + 75 Combine like terms: -75 + 75 = 0 0 + 1.1875t + t2 = 0 + 75 1.1875t + t2 = 0 + 75 Combine like terms: 0 + 75 = 75 1.1875t + t2 = 75 The t term is 1.1875t. Take half its coefficient (0.59375). Square it (0.3525390625) and add it to both sides. Add '0.3525390625' to each side of the equation. 1.1875t + 0.3525390625 + t2 = 75 + 0.3525390625 Reorder the terms: 0.3525390625 + 1.1875t + t2 = 75 + 0.3525390625 Combine like terms: 75 + 0.3525390625 = 75.3525390625 0.3525390625 + 1.1875t + t2 = 75.3525390625 Factor a perfect square on the left side: (t + 0.59375)(t + 0.59375) = 75.3525390625 Calculate the square root of the right side: 8.680584028 Break this problem into two subproblems by setting (t + 0.59375) equal to 8.680584028 and -8.680584028.Subproblem 1
t + 0.59375 = 8.680584028 Simplifying t + 0.59375 = 8.680584028 Reorder the terms: 0.59375 + t = 8.680584028 Solving 0.59375 + t = 8.680584028 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.59375' to each side of the equation. 0.59375 + -0.59375 + t = 8.680584028 + -0.59375 Combine like terms: 0.59375 + -0.59375 = 0.00000 0.00000 + t = 8.680584028 + -0.59375 t = 8.680584028 + -0.59375 Combine like terms: 8.680584028 + -0.59375 = 8.086834028 t = 8.086834028 Simplifying t = 8.086834028Subproblem 2
t + 0.59375 = -8.680584028 Simplifying t + 0.59375 = -8.680584028 Reorder the terms: 0.59375 + t = -8.680584028 Solving 0.59375 + t = -8.680584028 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.59375' to each side of the equation. 0.59375 + -0.59375 + t = -8.680584028 + -0.59375 Combine like terms: 0.59375 + -0.59375 = 0.00000 0.00000 + t = -8.680584028 + -0.59375 t = -8.680584028 + -0.59375 Combine like terms: -8.680584028 + -0.59375 = -9.274334028 t = -9.274334028 Simplifying t = -9.274334028Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.086834028, -9.274334028}
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