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Simplifying 25 = 4t + 5t2 Solving 25 = 4t + 5t2 Solving for variable 't'. Reorder the terms: 25 + -4t + -5t2 = 4t + -4t + 5t2 + -5t2 Combine like terms: 4t + -4t = 0 25 + -4t + -5t2 = 0 + 5t2 + -5t2 25 + -4t + -5t2 = 5t2 + -5t2 Combine like terms: 5t2 + -5t2 = 0 25 + -4t + -5t2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -5 + 0.8t + t2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + 0.8t + 5 + t2 = 0 + 5 Reorder the terms: -5 + 5 + 0.8t + t2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 0.8t + t2 = 0 + 5 0.8t + t2 = 0 + 5 Combine like terms: 0 + 5 = 5 0.8t + t2 = 5 The t term is 0.8t. Take half its coefficient (0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. 0.8t + 0.16 + t2 = 5 + 0.16 Reorder the terms: 0.16 + 0.8t + t2 = 5 + 0.16 Combine like terms: 5 + 0.16 = 5.16 0.16 + 0.8t + t2 = 5.16 Factor a perfect square on the left side: (t + 0.4)(t + 0.4) = 5.16 Calculate the square root of the right side: 2.271563338 Break this problem into two subproblems by setting (t + 0.4) equal to 2.271563338 and -2.271563338.Subproblem 1
t + 0.4 = 2.271563338 Simplifying t + 0.4 = 2.271563338 Reorder the terms: 0.4 + t = 2.271563338 Solving 0.4 + t = 2.271563338 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + t = 2.271563338 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + t = 2.271563338 + -0.4 t = 2.271563338 + -0.4 Combine like terms: 2.271563338 + -0.4 = 1.871563338 t = 1.871563338 Simplifying t = 1.871563338Subproblem 2
t + 0.4 = -2.271563338 Simplifying t + 0.4 = -2.271563338 Reorder the terms: 0.4 + t = -2.271563338 Solving 0.4 + t = -2.271563338 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + t = -2.271563338 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + t = -2.271563338 + -0.4 t = -2.271563338 + -0.4 Combine like terms: -2.271563338 + -0.4 = -2.671563338 t = -2.671563338 Simplifying t = -2.671563338Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.871563338, -2.671563338}
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