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Simplifying (t) = 100 + -2t2 t = 100 + -2t2 Solving t = 100 + -2t2 Solving for variable 't'. Reorder the terms: -100 + t + 2t2 = 100 + -2t2 + -100 + 2t2 Reorder the terms: -100 + t + 2t2 = 100 + -100 + -2t2 + 2t2 Combine like terms: 100 + -100 = 0 -100 + t + 2t2 = 0 + -2t2 + 2t2 -100 + t + 2t2 = -2t2 + 2t2 Combine like terms: -2t2 + 2t2 = 0 -100 + t + 2t2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -50 + 0.5t + t2 = 0 Move the constant term to the right: Add '50' to each side of the equation. -50 + 0.5t + 50 + t2 = 0 + 50 Reorder the terms: -50 + 50 + 0.5t + t2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + 0.5t + t2 = 0 + 50 0.5t + t2 = 0 + 50 Combine like terms: 0 + 50 = 50 0.5t + t2 = 50 The t term is t. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.5t + 0.25 + t2 = 50 + 0.25 Reorder the terms: 0.25 + 0.5t + t2 = 50 + 0.25 Combine like terms: 50 + 0.25 = 50.25 0.25 + 0.5t + t2 = 50.25 Factor a perfect square on the left side: (t + 0.5)(t + 0.5) = 50.25 Calculate the square root of the right side: 7.088723439 Break this problem into two subproblems by setting (t + 0.5) equal to 7.088723439 and -7.088723439.Subproblem 1
t + 0.5 = 7.088723439 Simplifying t + 0.5 = 7.088723439 Reorder the terms: 0.5 + t = 7.088723439 Solving 0.5 + t = 7.088723439 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + t = 7.088723439 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = 7.088723439 + -0.5 t = 7.088723439 + -0.5 Combine like terms: 7.088723439 + -0.5 = 6.588723439 t = 6.588723439 Simplifying t = 6.588723439Subproblem 2
t + 0.5 = -7.088723439 Simplifying t + 0.5 = -7.088723439 Reorder the terms: 0.5 + t = -7.088723439 Solving 0.5 + t = -7.088723439 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + t = -7.088723439 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = -7.088723439 + -0.5 t = -7.088723439 + -0.5 Combine like terms: -7.088723439 + -0.5 = -7.588723439 t = -7.588723439 Simplifying t = -7.588723439Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.588723439, -7.588723439}
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