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Simplifying 100t2 + 40t + 1 = 0 Reorder the terms: 1 + 40t + 100t2 = 0 Solving 1 + 40t + 100t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 100 the coefficient of the squared term: Divide each side by '100'. 0.01 + 0.4t + t2 = 0 Move the constant term to the right: Add '-0.01' to each side of the equation. 0.01 + 0.4t + -0.01 + t2 = 0 + -0.01 Reorder the terms: 0.01 + -0.01 + 0.4t + t2 = 0 + -0.01 Combine like terms: 0.01 + -0.01 = 0.00 0.00 + 0.4t + t2 = 0 + -0.01 0.4t + t2 = 0 + -0.01 Combine like terms: 0 + -0.01 = -0.01 0.4t + t2 = -0.01 The t term is 0.4t. Take half its coefficient (0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. 0.4t + 0.04 + t2 = -0.01 + 0.04 Reorder the terms: 0.04 + 0.4t + t2 = -0.01 + 0.04 Combine like terms: -0.01 + 0.04 = 0.03 0.04 + 0.4t + t2 = 0.03 Factor a perfect square on the left side: (t + 0.2)(t + 0.2) = 0.03 Calculate the square root of the right side: 0.173205081 Break this problem into two subproblems by setting (t + 0.2) equal to 0.173205081 and -0.173205081.Subproblem 1
t + 0.2 = 0.173205081 Simplifying t + 0.2 = 0.173205081 Reorder the terms: 0.2 + t = 0.173205081 Solving 0.2 + t = 0.173205081 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + t = 0.173205081 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + t = 0.173205081 + -0.2 t = 0.173205081 + -0.2 Combine like terms: 0.173205081 + -0.2 = -0.026794919 t = -0.026794919 Simplifying t = -0.026794919Subproblem 2
t + 0.2 = -0.173205081 Simplifying t + 0.2 = -0.173205081 Reorder the terms: 0.2 + t = -0.173205081 Solving 0.2 + t = -0.173205081 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + t = -0.173205081 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + t = -0.173205081 + -0.2 t = -0.173205081 + -0.2 Combine like terms: -0.173205081 + -0.2 = -0.373205081 t = -0.373205081 Simplifying t = -0.373205081Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.026794919, -0.373205081}
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