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Simplifying 400 = 0.5t2 + 5t Reorder the terms: 400 = 5t + 0.5t2 Solving 400 = 5t + 0.5t2 Solving for variable 't'. Reorder the terms: 400 + -5t + -0.5t2 = 5t + -5t + 0.5t2 + -0.5t2 Combine like terms: 5t + -5t = 0 400 + -5t + -0.5t2 = 0 + 0.5t2 + -0.5t2 400 + -5t + -0.5t2 = 0.5t2 + -0.5t2 Combine like terms: 0.5t2 + -0.5t2 = 0.0 400 + -5t + -0.5t2 = 0.0 Begin completing the square. Divide all terms by -0.5 the coefficient of the squared term: Divide each side by '-0.5'. -800 + 10t + t2 = 0 Move the constant term to the right: Add '800' to each side of the equation. -800 + 10t + 800 + t2 = 0 + 800 Reorder the terms: -800 + 800 + 10t + t2 = 0 + 800 Combine like terms: -800 + 800 = 0 0 + 10t + t2 = 0 + 800 10t + t2 = 0 + 800 Combine like terms: 0 + 800 = 800 10t + t2 = 800 The t term is 10t. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10t + 25 + t2 = 800 + 25 Reorder the terms: 25 + 10t + t2 = 800 + 25 Combine like terms: 800 + 25 = 825 25 + 10t + t2 = 825 Factor a perfect square on the left side: (t + 5)(t + 5) = 825 Calculate the square root of the right side: 28.722813233 Break this problem into two subproblems by setting (t + 5) equal to 28.722813233 and -28.722813233.Subproblem 1
t + 5 = 28.722813233 Simplifying t + 5 = 28.722813233 Reorder the terms: 5 + t = 28.722813233 Solving 5 + t = 28.722813233 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + t = 28.722813233 + -5 Combine like terms: 5 + -5 = 0 0 + t = 28.722813233 + -5 t = 28.722813233 + -5 Combine like terms: 28.722813233 + -5 = 23.722813233 t = 23.722813233 Simplifying t = 23.722813233Subproblem 2
t + 5 = -28.722813233 Simplifying t + 5 = -28.722813233 Reorder the terms: 5 + t = -28.722813233 Solving 5 + t = -28.722813233 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + t = -28.722813233 + -5 Combine like terms: 5 + -5 = 0 0 + t = -28.722813233 + -5 t = -28.722813233 + -5 Combine like terms: -28.722813233 + -5 = -33.722813233 t = -33.722813233 Simplifying t = -33.722813233Solution
The solution to the problem is based on the solutions from the subproblems. t = {23.722813233, -33.722813233}
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