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Simplifying 2t2 + 3t + -4 = 0 Reorder the terms: -4 + 3t + 2t2 = 0 Solving -4 + 3t + 2t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -2 + 1.5t + t2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 1.5t + 2 + t2 = 0 + 2 Reorder the terms: -2 + 2 + 1.5t + t2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 1.5t + t2 = 0 + 2 1.5t + t2 = 0 + 2 Combine like terms: 0 + 2 = 2 1.5t + t2 = 2 The t term is 1.5t. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5t + 0.5625 + t2 = 2 + 0.5625 Reorder the terms: 0.5625 + 1.5t + t2 = 2 + 0.5625 Combine like terms: 2 + 0.5625 = 2.5625 0.5625 + 1.5t + t2 = 2.5625 Factor a perfect square on the left side: (t + 0.75)(t + 0.75) = 2.5625 Calculate the square root of the right side: 1.600781059 Break this problem into two subproblems by setting (t + 0.75) equal to 1.600781059 and -1.600781059.Subproblem 1
t + 0.75 = 1.600781059 Simplifying t + 0.75 = 1.600781059 Reorder the terms: 0.75 + t = 1.600781059 Solving 0.75 + t = 1.600781059 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + t = 1.600781059 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + t = 1.600781059 + -0.75 t = 1.600781059 + -0.75 Combine like terms: 1.600781059 + -0.75 = 0.850781059 t = 0.850781059 Simplifying t = 0.850781059Subproblem 2
t + 0.75 = -1.600781059 Simplifying t + 0.75 = -1.600781059 Reorder the terms: 0.75 + t = -1.600781059 Solving 0.75 + t = -1.600781059 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + t = -1.600781059 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + t = -1.600781059 + -0.75 t = -1.600781059 + -0.75 Combine like terms: -1.600781059 + -0.75 = -2.350781059 t = -2.350781059 Simplifying t = -2.350781059Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.850781059, -2.350781059}
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