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Simplifying 100t2 + 6t + -27 = 0 Reorder the terms: -27 + 6t + 100t2 = 0 Solving -27 + 6t + 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'. -0.27 + 0.06t + t2 = 0 Move the constant term to the right: Add '0.27' to each side of the equation. -0.27 + 0.06t + 0.27 + t2 = 0 + 0.27 Reorder the terms: -0.27 + 0.27 + 0.06t + t2 = 0 + 0.27 Combine like terms: -0.27 + 0.27 = 0.00 0.00 + 0.06t + t2 = 0 + 0.27 0.06t + t2 = 0 + 0.27 Combine like terms: 0 + 0.27 = 0.27 0.06t + t2 = 0.27 The t term is 0.06t. Take half its coefficient (0.03). Square it (0.0009) and add it to both sides. Add '0.0009' to each side of the equation. 0.06t + 0.0009 + t2 = 0.27 + 0.0009 Reorder the terms: 0.0009 + 0.06t + t2 = 0.27 + 0.0009 Combine like terms: 0.27 + 0.0009 = 0.2709 0.0009 + 0.06t + t2 = 0.2709 Factor a perfect square on the left side: (t + 0.03)(t + 0.03) = 0.2709 Calculate the square root of the right side: 0.520480547 Break this problem into two subproblems by setting (t + 0.03) equal to 0.520480547 and -0.520480547.Subproblem 1
t + 0.03 = 0.520480547 Simplifying t + 0.03 = 0.520480547 Reorder the terms: 0.03 + t = 0.520480547 Solving 0.03 + t = 0.520480547 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.03' to each side of the equation. 0.03 + -0.03 + t = 0.520480547 + -0.03 Combine like terms: 0.03 + -0.03 = 0.00 0.00 + t = 0.520480547 + -0.03 t = 0.520480547 + -0.03 Combine like terms: 0.520480547 + -0.03 = 0.490480547 t = 0.490480547 Simplifying t = 0.490480547Subproblem 2
t + 0.03 = -0.520480547 Simplifying t + 0.03 = -0.520480547 Reorder the terms: 0.03 + t = -0.520480547 Solving 0.03 + t = -0.520480547 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.03' to each side of the equation. 0.03 + -0.03 + t = -0.520480547 + -0.03 Combine like terms: 0.03 + -0.03 = 0.00 0.00 + t = -0.520480547 + -0.03 t = -0.520480547 + -0.03 Combine like terms: -0.520480547 + -0.03 = -0.550480547 t = -0.550480547 Simplifying t = -0.550480547Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.490480547, -0.550480547}
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