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Simplifying -16t2 + 19t + 2 = 0 Reorder the terms: 2 + 19t + -16t2 = 0 Solving 2 + 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'. -0.125 + -1.1875t + t2 = 0 Move the constant term to the right: Add '0.125' to each side of the equation. -0.125 + -1.1875t + 0.125 + t2 = 0 + 0.125 Reorder the terms: -0.125 + 0.125 + -1.1875t + t2 = 0 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + -1.1875t + t2 = 0 + 0.125 -1.1875t + t2 = 0 + 0.125 Combine like terms: 0 + 0.125 = 0.125 -1.1875t + t2 = 0.125 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 = 0.125 + 0.3525390625 Reorder the terms: 0.3525390625 + -1.1875t + t2 = 0.125 + 0.3525390625 Combine like terms: 0.125 + 0.3525390625 = 0.4775390625 0.3525390625 + -1.1875t + t2 = 0.4775390625 Factor a perfect square on the left side: (t + -0.59375)(t + -0.59375) = 0.4775390625 Calculate the square root of the right side: 0.691042012 Break this problem into two subproblems by setting (t + -0.59375) equal to 0.691042012 and -0.691042012.Subproblem 1
t + -0.59375 = 0.691042012 Simplifying t + -0.59375 = 0.691042012 Reorder the terms: -0.59375 + t = 0.691042012 Solving -0.59375 + t = 0.691042012 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 = 0.691042012 + 0.59375 Combine like terms: -0.59375 + 0.59375 = 0.00000 0.00000 + t = 0.691042012 + 0.59375 t = 0.691042012 + 0.59375 Combine like terms: 0.691042012 + 0.59375 = 1.284792012 t = 1.284792012 Simplifying t = 1.284792012Subproblem 2
t + -0.59375 = -0.691042012 Simplifying t + -0.59375 = -0.691042012 Reorder the terms: -0.59375 + t = -0.691042012 Solving -0.59375 + t = -0.691042012 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 = -0.691042012 + 0.59375 Combine like terms: -0.59375 + 0.59375 = 0.00000 0.00000 + t = -0.691042012 + 0.59375 t = -0.691042012 + 0.59375 Combine like terms: -0.691042012 + 0.59375 = -0.097292012 t = -0.097292012 Simplifying t = -0.097292012Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.284792012, -0.097292012}
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