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Simplifying 5 = 4t + -0.8t2 Solving 5 = 4t + -0.8t2 Solving for variable 't'. Reorder the terms: 5 + -4t + 0.8t2 = 4t + -4t + -0.8t2 + 0.8t2 Combine like terms: 4t + -4t = 0 5 + -4t + 0.8t2 = 0 + -0.8t2 + 0.8t2 5 + -4t + 0.8t2 = -0.8t2 + 0.8t2 Combine like terms: -0.8t2 + 0.8t2 = 0.0 5 + -4t + 0.8t2 = 0.0 Begin completing the square. Divide all terms by 0.8 the coefficient of the squared term: Divide each side by '0.8'. 6.25 + -5t + t2 = 0 Move the constant term to the right: Add '-6.25' to each side of the equation. 6.25 + -5t + -6.25 + t2 = 0 + -6.25 Reorder the terms: 6.25 + -6.25 + -5t + t2 = 0 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 0.00 + -5t + t2 = 0 + -6.25 -5t + t2 = 0 + -6.25 Combine like terms: 0 + -6.25 = -6.25 -5t + t2 = -6.25 The t term is -5t. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5t + 6.25 + t2 = -6.25 + 6.25 Reorder the terms: 6.25 + -5t + t2 = -6.25 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 6.25 + -5t + t2 = 0.00 Factor a perfect square on the left side: (t + -2.5)(t + -2.5) = 0.00 Calculate the square root of the right side: 0.00 Break this problem into two subproblems by setting (t + -2.5) equal to 0.00 and 0.00.Subproblem 1
t + -2.5 = 0.00 Simplifying t + -2.5 = 0.00 Reorder the terms: -2.5 + t = 0.00 Solving -2.5 + t = 0.00 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + t = 0.00 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + t = 0.00 + 2.5 t = 0.00 + 2.5 Combine like terms: 0.00 + 2.5 = 2.5 t = 2.5 Simplifying t = 2.5Subproblem 2
t + -2.5 = 0.00 Simplifying t + -2.5 = 0.00 Reorder the terms: -2.5 + t = 0.00 Solving -2.5 + t = 0.00 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + t = 0.00 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + t = 0.00 + 2.5 t = 0.00 + 2.5 Combine like terms: 0.00 + 2.5 = 2.5 t = 2.5 Simplifying t = 2.5Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.5, 2.5}
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