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Simplifying 0 = 5t2 + -4t + -3 Reorder the terms: 0 = -3 + -4t + 5t2 Solving 0 = -3 + -4t + 5t2 Solving for variable 't'. Combine like terms: 0 + 3 = 3 3 + 4t + -5t2 = -3 + -4t + 5t2 + 3 + 4t + -5t2 Reorder the terms: 3 + 4t + -5t2 = -3 + 3 + -4t + 4t + 5t2 + -5t2 Combine like terms: -3 + 3 = 0 3 + 4t + -5t2 = 0 + -4t + 4t + 5t2 + -5t2 3 + 4t + -5t2 = -4t + 4t + 5t2 + -5t2 Combine like terms: -4t + 4t = 0 3 + 4t + -5t2 = 0 + 5t2 + -5t2 3 + 4t + -5t2 = 5t2 + -5t2 Combine like terms: 5t2 + -5t2 = 0 3 + 4t + -5t2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -0.6 + -0.8t + t2 = 0 Move the constant term to the right: Add '0.6' to each side of the equation. -0.6 + -0.8t + 0.6 + t2 = 0 + 0.6 Reorder the terms: -0.6 + 0.6 + -0.8t + t2 = 0 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + -0.8t + t2 = 0 + 0.6 -0.8t + t2 = 0 + 0.6 Combine like terms: 0 + 0.6 = 0.6 -0.8t + t2 = 0.6 The t term is -0.8t. Take half its coefficient (-0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. -0.8t + 0.16 + t2 = 0.6 + 0.16 Reorder the terms: 0.16 + -0.8t + t2 = 0.6 + 0.16 Combine like terms: 0.6 + 0.16 = 0.76 0.16 + -0.8t + t2 = 0.76 Factor a perfect square on the left side: (t + -0.4)(t + -0.4) = 0.76 Calculate the square root of the right side: 0.871779789 Break this problem into two subproblems by setting (t + -0.4) equal to 0.871779789 and -0.871779789.Subproblem 1
t + -0.4 = 0.871779789 Simplifying t + -0.4 = 0.871779789 Reorder the terms: -0.4 + t = 0.871779789 Solving -0.4 + t = 0.871779789 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + t = 0.871779789 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + t = 0.871779789 + 0.4 t = 0.871779789 + 0.4 Combine like terms: 0.871779789 + 0.4 = 1.271779789 t = 1.271779789 Simplifying t = 1.271779789Subproblem 2
t + -0.4 = -0.871779789 Simplifying t + -0.4 = -0.871779789 Reorder the terms: -0.4 + t = -0.871779789 Solving -0.4 + t = -0.871779789 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + t = -0.871779789 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + t = -0.871779789 + 0.4 t = -0.871779789 + 0.4 Combine like terms: -0.871779789 + 0.4 = -0.471779789 t = -0.471779789 Simplifying t = -0.471779789Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.271779789, -0.471779789}
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