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Simplifying -2.4 = 5.9t + (-4.905) * t2 Solving -2.4 = 5.9t + -4.905t2 Solving for variable 't'. Reorder the terms: -2.4 + -5.9t + 4.905t2 = 5.9t + -5.9t + -4.905t2 + 4.905t2 Combine like terms: 5.9t + -5.9t = 0.0 -2.4 + -5.9t + 4.905t2 = 0.0 + -4.905t2 + 4.905t2 -2.4 + -5.9t + 4.905t2 = -4.905t2 + 4.905t2 Combine like terms: -4.905t2 + 4.905t2 = 0.000 -2.4 + -5.9t + 4.905t2 = 0.000 Begin completing the square. Divide all terms by 4.905 the coefficient of the squared term: Divide each side by '4.905'. -0.4892966361 + -1.20285423t + t2 = 0 Move the constant term to the right: Add '0.4892966361' to each side of the equation. -0.4892966361 + -1.20285423t + 0.4892966361 + t2 = 0 + 0.4892966361 Reorder the terms: -0.4892966361 + 0.4892966361 + -1.20285423t + t2 = 0 + 0.4892966361 Combine like terms: -0.4892966361 + 0.4892966361 = 0.0000000000 0.0000000000 + -1.20285423t + t2 = 0 + 0.4892966361 -1.20285423t + t2 = 0 + 0.4892966361 Combine like terms: 0 + 0.4892966361 = 0.4892966361 -1.20285423t + t2 = 0.4892966361 The t term is -1.20285423t. Take half its coefficient (-0.601427115). Square it (0.3617145747) and add it to both sides. Add '0.3617145747' to each side of the equation. -1.20285423t + 0.3617145747 + t2 = 0.4892966361 + 0.3617145747 Reorder the terms: 0.3617145747 + -1.20285423t + t2 = 0.4892966361 + 0.3617145747 Combine like terms: 0.4892966361 + 0.3617145747 = 0.8510112108 0.3617145747 + -1.20285423t + t2 = 0.8510112108 Factor a perfect square on the left side: (t + -0.601427115)(t + -0.601427115) = 0.8510112108 Calculate the square root of the right side: 0.922502689 Break this problem into two subproblems by setting (t + -0.601427115) equal to 0.922502689 and -0.922502689.Subproblem 1
t + -0.601427115 = 0.922502689 Simplifying t + -0.601427115 = 0.922502689 Reorder the terms: -0.601427115 + t = 0.922502689 Solving -0.601427115 + t = 0.922502689 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.601427115' to each side of the equation. -0.601427115 + 0.601427115 + t = 0.922502689 + 0.601427115 Combine like terms: -0.601427115 + 0.601427115 = 0.000000000 0.000000000 + t = 0.922502689 + 0.601427115 t = 0.922502689 + 0.601427115 Combine like terms: 0.922502689 + 0.601427115 = 1.523929804 t = 1.523929804 Simplifying t = 1.523929804Subproblem 2
t + -0.601427115 = -0.922502689 Simplifying t + -0.601427115 = -0.922502689 Reorder the terms: -0.601427115 + t = -0.922502689 Solving -0.601427115 + t = -0.922502689 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.601427115' to each side of the equation. -0.601427115 + 0.601427115 + t = -0.922502689 + 0.601427115 Combine like terms: -0.601427115 + 0.601427115 = 0.000000000 0.000000000 + t = -0.922502689 + 0.601427115 t = -0.922502689 + 0.601427115 Combine like terms: -0.922502689 + 0.601427115 = -0.321075574 t = -0.321075574 Simplifying t = -0.321075574Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.523929804, -0.321075574}
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