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Simplifying 7.4 = t2 + -4t + -9.333 Reorder the terms: 7.4 = -9.333 + -4t + t2 Solving 7.4 = -9.333 + -4t + t2 Solving for variable 't'. Combine like terms: 7.4 + 9.333 = 16.733 16.733 + 4t + -1t2 = -9.333 + -4t + t2 + 9.333 + 4t + -1t2 Reorder the terms: 16.733 + 4t + -1t2 = -9.333 + 9.333 + -4t + 4t + t2 + -1t2 Combine like terms: -9.333 + 9.333 = 0.000 16.733 + 4t + -1t2 = 0.000 + -4t + 4t + t2 + -1t2 16.733 + 4t + -1t2 = -4t + 4t + t2 + -1t2 Combine like terms: -4t + 4t = 0 16.733 + 4t + -1t2 = 0 + t2 + -1t2 16.733 + 4t + -1t2 = t2 + -1t2 Combine like terms: t2 + -1t2 = 0 16.733 + 4t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -16.733 + -4t + t2 = 0 Move the constant term to the right: Add '16.733' to each side of the equation. -16.733 + -4t + 16.733 + t2 = 0 + 16.733 Reorder the terms: -16.733 + 16.733 + -4t + t2 = 0 + 16.733 Combine like terms: -16.733 + 16.733 = 0.000 0.000 + -4t + t2 = 0 + 16.733 -4t + t2 = 0 + 16.733 Combine like terms: 0 + 16.733 = 16.733 -4t + t2 = 16.733 The t term is -4t. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4t + 4 + t2 = 16.733 + 4 Reorder the terms: 4 + -4t + t2 = 16.733 + 4 Combine like terms: 16.733 + 4 = 20.733 4 + -4t + t2 = 20.733 Factor a perfect square on the left side: (t + -2)(t + -2) = 20.733 Calculate the square root of the right side: 4.553350415 Break this problem into two subproblems by setting (t + -2) equal to 4.553350415 and -4.553350415.Subproblem 1
t + -2 = 4.553350415 Simplifying t + -2 = 4.553350415 Reorder the terms: -2 + t = 4.553350415 Solving -2 + t = 4.553350415 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + t = 4.553350415 + 2 Combine like terms: -2 + 2 = 0 0 + t = 4.553350415 + 2 t = 4.553350415 + 2 Combine like terms: 4.553350415 + 2 = 6.553350415 t = 6.553350415 Simplifying t = 6.553350415Subproblem 2
t + -2 = -4.553350415 Simplifying t + -2 = -4.553350415 Reorder the terms: -2 + t = -4.553350415 Solving -2 + t = -4.553350415 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + t = -4.553350415 + 2 Combine like terms: -2 + 2 = 0 0 + t = -4.553350415 + 2 t = -4.553350415 + 2 Combine like terms: -4.553350415 + 2 = -2.553350415 t = -2.553350415 Simplifying t = -2.553350415Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.553350415, -2.553350415}
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