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Simplifying 0.07t2 + 0.84t + 1.5 = 0 Reorder the terms: 1.5 + 0.84t + 0.07t2 = 0 Solving 1.5 + 0.84t + 0.07t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 0.07 the coefficient of the squared term: Divide each side by '0.07'. 21.42857143 + 12t + t2 = 0 Move the constant term to the right: Add '-21.42857143' to each side of the equation. 21.42857143 + 12t + -21.42857143 + t2 = 0 + -21.42857143 Reorder the terms: 21.42857143 + -21.42857143 + 12t + t2 = 0 + -21.42857143 Combine like terms: 21.42857143 + -21.42857143 = 0.00000000 0.00000000 + 12t + t2 = 0 + -21.42857143 12t + t2 = 0 + -21.42857143 Combine like terms: 0 + -21.42857143 = -21.42857143 12t + t2 = -21.42857143 The t term is 12t. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12t + 36 + t2 = -21.42857143 + 36 Reorder the terms: 36 + 12t + t2 = -21.42857143 + 36 Combine like terms: -21.42857143 + 36 = 14.57142857 36 + 12t + t2 = 14.57142857 Factor a perfect square on the left side: (t + 6)(t + 6) = 14.57142857 Calculate the square root of the right side: 3.817254061 Break this problem into two subproblems by setting (t + 6) equal to 3.817254061 and -3.817254061.Subproblem 1
t + 6 = 3.817254061 Simplifying t + 6 = 3.817254061 Reorder the terms: 6 + t = 3.817254061 Solving 6 + t = 3.817254061 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + t = 3.817254061 + -6 Combine like terms: 6 + -6 = 0 0 + t = 3.817254061 + -6 t = 3.817254061 + -6 Combine like terms: 3.817254061 + -6 = -2.182745939 t = -2.182745939 Simplifying t = -2.182745939Subproblem 2
t + 6 = -3.817254061 Simplifying t + 6 = -3.817254061 Reorder the terms: 6 + t = -3.817254061 Solving 6 + t = -3.817254061 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + t = -3.817254061 + -6 Combine like terms: 6 + -6 = 0 0 + t = -3.817254061 + -6 t = -3.817254061 + -6 Combine like terms: -3.817254061 + -6 = -9.817254061 t = -9.817254061 Simplifying t = -9.817254061Solution
The solution to the problem is based on the solutions from the subproblems. t = {-2.182745939, -9.817254061}
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