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Simplifying 0 = -16t2 + -19t + 150 Reorder the terms: 0 = 150 + -19t + -16t2 Solving 0 = 150 + -19t + -16t2 Solving for variable 't'. Combine like terms: 0 + -150 = -150 -150 + 19t + 16t2 = 150 + -19t + -16t2 + -150 + 19t + 16t2 Reorder the terms: -150 + 19t + 16t2 = 150 + -150 + -19t + 19t + -16t2 + 16t2 Combine like terms: 150 + -150 = 0 -150 + 19t + 16t2 = 0 + -19t + 19t + -16t2 + 16t2 -150 + 19t + 16t2 = -19t + 19t + -16t2 + 16t2 Combine like terms: -19t + 19t = 0 -150 + 19t + 16t2 = 0 + -16t2 + 16t2 -150 + 19t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -150 + 19t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -9.375 + 1.1875t + t2 = 0 Move the constant term to the right: Add '9.375' to each side of the equation. -9.375 + 1.1875t + 9.375 + t2 = 0 + 9.375 Reorder the terms: -9.375 + 9.375 + 1.1875t + t2 = 0 + 9.375 Combine like terms: -9.375 + 9.375 = 0.000 0.000 + 1.1875t + t2 = 0 + 9.375 1.1875t + t2 = 0 + 9.375 Combine like terms: 0 + 9.375 = 9.375 1.1875t + t2 = 9.375 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 = 9.375 + 0.3525390625 Reorder the terms: 0.3525390625 + 1.1875t + t2 = 9.375 + 0.3525390625 Combine like terms: 9.375 + 0.3525390625 = 9.7275390625 0.3525390625 + 1.1875t + t2 = 9.7275390625 Factor a perfect square on the left side: (t + 0.59375)(t + 0.59375) = 9.7275390625 Calculate the square root of the right side: 3.118900297 Break this problem into two subproblems by setting (t + 0.59375) equal to 3.118900297 and -3.118900297.Subproblem 1
t + 0.59375 = 3.118900297 Simplifying t + 0.59375 = 3.118900297 Reorder the terms: 0.59375 + t = 3.118900297 Solving 0.59375 + t = 3.118900297 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 = 3.118900297 + -0.59375 Combine like terms: 0.59375 + -0.59375 = 0.00000 0.00000 + t = 3.118900297 + -0.59375 t = 3.118900297 + -0.59375 Combine like terms: 3.118900297 + -0.59375 = 2.525150297 t = 2.525150297 Simplifying t = 2.525150297Subproblem 2
t + 0.59375 = -3.118900297 Simplifying t + 0.59375 = -3.118900297 Reorder the terms: 0.59375 + t = -3.118900297 Solving 0.59375 + t = -3.118900297 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 = -3.118900297 + -0.59375 Combine like terms: 0.59375 + -0.59375 = 0.00000 0.00000 + t = -3.118900297 + -0.59375 t = -3.118900297 + -0.59375 Combine like terms: -3.118900297 + -0.59375 = -3.712650297 t = -3.712650297 Simplifying t = -3.712650297Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.525150297, -3.712650297}
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