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Simplifying 0.9 = 4t + -1t2 Solving 0.9 = 4t + -1t2 Solving for variable 't'. Reorder the terms: 0.9 + -4t + t2 = 4t + -4t + -1t2 + t2 Combine like terms: 4t + -4t = 0 0.9 + -4t + t2 = 0 + -1t2 + t2 0.9 + -4t + t2 = -1t2 + t2 Combine like terms: -1t2 + t2 = 0 0.9 + -4t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-0.9' to each side of the equation. 0.9 + -4t + -0.9 + t2 = 0 + -0.9 Reorder the terms: 0.9 + -0.9 + -4t + t2 = 0 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + -4t + t2 = 0 + -0.9 -4t + t2 = 0 + -0.9 Combine like terms: 0 + -0.9 = -0.9 -4t + t2 = -0.9 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 = -0.9 + 4 Reorder the terms: 4 + -4t + t2 = -0.9 + 4 Combine like terms: -0.9 + 4 = 3.1 4 + -4t + t2 = 3.1 Factor a perfect square on the left side: (t + -2)(t + -2) = 3.1 Calculate the square root of the right side: 1.760681686 Break this problem into two subproblems by setting (t + -2) equal to 1.760681686 and -1.760681686.Subproblem 1
t + -2 = 1.760681686 Simplifying t + -2 = 1.760681686 Reorder the terms: -2 + t = 1.760681686 Solving -2 + t = 1.760681686 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 = 1.760681686 + 2 Combine like terms: -2 + 2 = 0 0 + t = 1.760681686 + 2 t = 1.760681686 + 2 Combine like terms: 1.760681686 + 2 = 3.760681686 t = 3.760681686 Simplifying t = 3.760681686Subproblem 2
t + -2 = -1.760681686 Simplifying t + -2 = -1.760681686 Reorder the terms: -2 + t = -1.760681686 Solving -2 + t = -1.760681686 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 = -1.760681686 + 2 Combine like terms: -2 + 2 = 0 0 + t = -1.760681686 + 2 t = -1.760681686 + 2 Combine like terms: -1.760681686 + 2 = 0.239318314 t = 0.239318314 Simplifying t = 0.239318314Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.760681686, 0.239318314}
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