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Simplifying -16t2 + 21t + -6 = 0 Reorder the terms: -6 + 21t + -16t2 = 0 Solving -6 + 21t + -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'. 0.375 + -1.3125t + t2 = 0 Move the constant term to the right: Add '-0.375' to each side of the equation. 0.375 + -1.3125t + -0.375 + t2 = 0 + -0.375 Reorder the terms: 0.375 + -0.375 + -1.3125t + t2 = 0 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + -1.3125t + t2 = 0 + -0.375 -1.3125t + t2 = 0 + -0.375 Combine like terms: 0 + -0.375 = -0.375 -1.3125t + t2 = -0.375 The t term is -1.3125t. Take half its coefficient (-0.65625). Square it (0.4306640625) and add it to both sides. Add '0.4306640625' to each side of the equation. -1.3125t + 0.4306640625 + t2 = -0.375 + 0.4306640625 Reorder the terms: 0.4306640625 + -1.3125t + t2 = -0.375 + 0.4306640625 Combine like terms: -0.375 + 0.4306640625 = 0.0556640625 0.4306640625 + -1.3125t + t2 = 0.0556640625 Factor a perfect square on the left side: (t + -0.65625)(t + -0.65625) = 0.0556640625 Calculate the square root of the right side: 0.235932326 Break this problem into two subproblems by setting (t + -0.65625) equal to 0.235932326 and -0.235932326.Subproblem 1
t + -0.65625 = 0.235932326 Simplifying t + -0.65625 = 0.235932326 Reorder the terms: -0.65625 + t = 0.235932326 Solving -0.65625 + t = 0.235932326 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.65625' to each side of the equation. -0.65625 + 0.65625 + t = 0.235932326 + 0.65625 Combine like terms: -0.65625 + 0.65625 = 0.00000 0.00000 + t = 0.235932326 + 0.65625 t = 0.235932326 + 0.65625 Combine like terms: 0.235932326 + 0.65625 = 0.892182326 t = 0.892182326 Simplifying t = 0.892182326Subproblem 2
t + -0.65625 = -0.235932326 Simplifying t + -0.65625 = -0.235932326 Reorder the terms: -0.65625 + t = -0.235932326 Solving -0.65625 + t = -0.235932326 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.65625' to each side of the equation. -0.65625 + 0.65625 + t = -0.235932326 + 0.65625 Combine like terms: -0.65625 + 0.65625 = 0.00000 0.00000 + t = -0.235932326 + 0.65625 t = -0.235932326 + 0.65625 Combine like terms: -0.235932326 + 0.65625 = 0.420317674 t = 0.420317674 Simplifying t = 0.420317674Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.892182326, 0.420317674}
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