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Simplifying 5t2 + 0.8t + -0.4 = 0 Reorder the terms: -0.4 + 0.8t + 5t2 = 0 Solving -0.4 + 0.8t + 5t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.08 + 0.16t + t2 = 0 Move the constant term to the right: Add '0.08' to each side of the equation. -0.08 + 0.16t + 0.08 + t2 = 0 + 0.08 Reorder the terms: -0.08 + 0.08 + 0.16t + t2 = 0 + 0.08 Combine like terms: -0.08 + 0.08 = 0.00 0.00 + 0.16t + t2 = 0 + 0.08 0.16t + t2 = 0 + 0.08 Combine like terms: 0 + 0.08 = 0.08 0.16t + t2 = 0.08 The t term is 0.16t. Take half its coefficient (0.08). Square it (0.0064) and add it to both sides. Add '0.0064' to each side of the equation. 0.16t + 0.0064 + t2 = 0.08 + 0.0064 Reorder the terms: 0.0064 + 0.16t + t2 = 0.08 + 0.0064 Combine like terms: 0.08 + 0.0064 = 0.0864 0.0064 + 0.16t + t2 = 0.0864 Factor a perfect square on the left side: (t + 0.08)(t + 0.08) = 0.0864 Calculate the square root of the right side: 0.293938769 Break this problem into two subproblems by setting (t + 0.08) equal to 0.293938769 and -0.293938769.Subproblem 1
t + 0.08 = 0.293938769 Simplifying t + 0.08 = 0.293938769 Reorder the terms: 0.08 + t = 0.293938769 Solving 0.08 + t = 0.293938769 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.08' to each side of the equation. 0.08 + -0.08 + t = 0.293938769 + -0.08 Combine like terms: 0.08 + -0.08 = 0.00 0.00 + t = 0.293938769 + -0.08 t = 0.293938769 + -0.08 Combine like terms: 0.293938769 + -0.08 = 0.213938769 t = 0.213938769 Simplifying t = 0.213938769Subproblem 2
t + 0.08 = -0.293938769 Simplifying t + 0.08 = -0.293938769 Reorder the terms: 0.08 + t = -0.293938769 Solving 0.08 + t = -0.293938769 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.08' to each side of the equation. 0.08 + -0.08 + t = -0.293938769 + -0.08 Combine like terms: 0.08 + -0.08 = 0.00 0.00 + t = -0.293938769 + -0.08 t = -0.293938769 + -0.08 Combine like terms: -0.293938769 + -0.08 = -0.373938769 t = -0.373938769 Simplifying t = -0.373938769Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.213938769, -0.373938769}
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