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Simplifying 2 = 5t2 + 6t Reorder the terms: 2 = 6t + 5t2 Solving 2 = 6t + 5t2 Solving for variable 't'. Reorder the terms: 2 + -6t + -5t2 = 6t + -6t + 5t2 + -5t2 Combine like terms: 6t + -6t = 0 2 + -6t + -5t2 = 0 + 5t2 + -5t2 2 + -6t + -5t2 = 5t2 + -5t2 Combine like terms: 5t2 + -5t2 = 0 2 + -6t + -5t2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -0.4 + 1.2t + t2 = 0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + 1.2t + 0.4 + t2 = 0 + 0.4 Reorder the terms: -0.4 + 0.4 + 1.2t + t2 = 0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + 1.2t + t2 = 0 + 0.4 1.2t + t2 = 0 + 0.4 Combine like terms: 0 + 0.4 = 0.4 1.2t + t2 = 0.4 The t term is 1.2t. Take half its coefficient (0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. 1.2t + 0.36 + t2 = 0.4 + 0.36 Reorder the terms: 0.36 + 1.2t + t2 = 0.4 + 0.36 Combine like terms: 0.4 + 0.36 = 0.76 0.36 + 1.2t + t2 = 0.76 Factor a perfect square on the left side: (t + 0.6)(t + 0.6) = 0.76 Calculate the square root of the right side: 0.871779789 Break this problem into two subproblems by setting (t + 0.6) equal to 0.871779789 and -0.871779789.Subproblem 1
t + 0.6 = 0.871779789 Simplifying t + 0.6 = 0.871779789 Reorder the terms: 0.6 + t = 0.871779789 Solving 0.6 + t = 0.871779789 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + t = 0.871779789 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + t = 0.871779789 + -0.6 t = 0.871779789 + -0.6 Combine like terms: 0.871779789 + -0.6 = 0.271779789 t = 0.271779789 Simplifying t = 0.271779789Subproblem 2
t + 0.6 = -0.871779789 Simplifying t + 0.6 = -0.871779789 Reorder the terms: 0.6 + t = -0.871779789 Solving 0.6 + t = -0.871779789 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + t = -0.871779789 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + t = -0.871779789 + -0.6 t = -0.871779789 + -0.6 Combine like terms: -0.871779789 + -0.6 = -1.471779789 t = -1.471779789 Simplifying t = -1.471779789Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.271779789, -1.471779789}
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