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Simplifying 0 = -5.2t2 + 15t + 8 Reorder the terms: 0 = 8 + 15t + -5.2t2 Solving 0 = 8 + 15t + -5.2t2 Solving for variable 't'. Combine like terms: 0 + -8 = -8 -8 + -15t + 5.2t2 = 8 + 15t + -5.2t2 + -8 + -15t + 5.2t2 Reorder the terms: -8 + -15t + 5.2t2 = 8 + -8 + 15t + -15t + -5.2t2 + 5.2t2 Combine like terms: 8 + -8 = 0 -8 + -15t + 5.2t2 = 0 + 15t + -15t + -5.2t2 + 5.2t2 -8 + -15t + 5.2t2 = 15t + -15t + -5.2t2 + 5.2t2 Combine like terms: 15t + -15t = 0 -8 + -15t + 5.2t2 = 0 + -5.2t2 + 5.2t2 -8 + -15t + 5.2t2 = -5.2t2 + 5.2t2 Combine like terms: -5.2t2 + 5.2t2 = 0.0 -8 + -15t + 5.2t2 = 0.0 Begin completing the square. Divide all terms by 5.2 the coefficient of the squared term: Divide each side by '5.2'. -1.538461538 + -2.884615385t + t2 = 0 Move the constant term to the right: Add '1.538461538' to each side of the equation. -1.538461538 + -2.884615385t + 1.538461538 + t2 = 0 + 1.538461538 Reorder the terms: -1.538461538 + 1.538461538 + -2.884615385t + t2 = 0 + 1.538461538 Combine like terms: -1.538461538 + 1.538461538 = 0.000000000 0.000000000 + -2.884615385t + t2 = 0 + 1.538461538 -2.884615385t + t2 = 0 + 1.538461538 Combine like terms: 0 + 1.538461538 = 1.538461538 -2.884615385t + t2 = 1.538461538 The t term is -2.884615385t. Take half its coefficient (-1.442307693). Square it (2.080251481) and add it to both sides. Add '2.080251481' to each side of the equation. -2.884615385t + 2.080251481 + t2 = 1.538461538 + 2.080251481 Reorder the terms: 2.080251481 + -2.884615385t + t2 = 1.538461538 + 2.080251481 Combine like terms: 1.538461538 + 2.080251481 = 3.618713019 2.080251481 + -2.884615385t + t2 = 3.618713019 Factor a perfect square on the left side: (t + -1.442307693)(t + -1.442307693) = 3.618713019 Calculate the square root of the right side: 1.902291518 Break this problem into two subproblems by setting (t + -1.442307693) equal to 1.902291518 and -1.902291518.Subproblem 1
t + -1.442307693 = 1.902291518 Simplifying t + -1.442307693 = 1.902291518 Reorder the terms: -1.442307693 + t = 1.902291518 Solving -1.442307693 + t = 1.902291518 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.442307693' to each side of the equation. -1.442307693 + 1.442307693 + t = 1.902291518 + 1.442307693 Combine like terms: -1.442307693 + 1.442307693 = 0.000000000 0.000000000 + t = 1.902291518 + 1.442307693 t = 1.902291518 + 1.442307693 Combine like terms: 1.902291518 + 1.442307693 = 3.344599211 t = 3.344599211 Simplifying t = 3.344599211Subproblem 2
t + -1.442307693 = -1.902291518 Simplifying t + -1.442307693 = -1.902291518 Reorder the terms: -1.442307693 + t = -1.902291518 Solving -1.442307693 + t = -1.902291518 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.442307693' to each side of the equation. -1.442307693 + 1.442307693 + t = -1.902291518 + 1.442307693 Combine like terms: -1.442307693 + 1.442307693 = 0.000000000 0.000000000 + t = -1.902291518 + 1.442307693 t = -1.902291518 + 1.442307693 Combine like terms: -1.902291518 + 1.442307693 = -0.459983825 t = -0.459983825 Simplifying t = -0.459983825Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.344599211, -0.459983825}
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