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Simplifying 2 + 6t + -5t2 = 0 Solving 2 + 6t + -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'. -0.4 + -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 = 1.471779789 t = 1.471779789 Simplifying t = 1.471779789Subproblem 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 = -0.271779789 t = -0.271779789 Simplifying t = -0.271779789Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.471779789, -0.271779789}
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