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Simplifying 16t2 + 32t = 1.44 Reorder the terms: 32t + 16t2 = 1.44 Solving 32t + 16t2 = 1.44 Solving for variable 't'. Reorder the terms: -1.44 + 32t + 16t2 = 1.44 + -1.44 Combine like terms: 1.44 + -1.44 = 0.00 -1.44 + 32t + 16t2 = 0.00 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.09 + 2t + t2 = 0.00 Move the constant term to the right: Add '0.09' to each side of the equation. -0.09 + 2t + 0.09 + t2 = 0.00 + 0.09 Reorder the terms: -0.09 + 0.09 + 2t + t2 = 0.00 + 0.09 Combine like terms: -0.09 + 0.09 = 0.00 0.00 + 2t + t2 = 0.00 + 0.09 2t + t2 = 0.00 + 0.09 Combine like terms: 0.00 + 0.09 = 0.09 2t + t2 = 0.09 The t term is 2t. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2t + 1 + t2 = 0.09 + 1 Reorder the terms: 1 + 2t + t2 = 0.09 + 1 Combine like terms: 0.09 + 1 = 1.09 1 + 2t + t2 = 1.09 Factor a perfect square on the left side: (t + 1)(t + 1) = 1.09 Calculate the square root of the right side: 1.044030651 Break this problem into two subproblems by setting (t + 1) equal to 1.044030651 and -1.044030651.Subproblem 1
t + 1 = 1.044030651 Simplifying t + 1 = 1.044030651 Reorder the terms: 1 + t = 1.044030651 Solving 1 + t = 1.044030651 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + t = 1.044030651 + -1 Combine like terms: 1 + -1 = 0 0 + t = 1.044030651 + -1 t = 1.044030651 + -1 Combine like terms: 1.044030651 + -1 = 0.044030651 t = 0.044030651 Simplifying t = 0.044030651Subproblem 2
t + 1 = -1.044030651 Simplifying t + 1 = -1.044030651 Reorder the terms: 1 + t = -1.044030651 Solving 1 + t = -1.044030651 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + t = -1.044030651 + -1 Combine like terms: 1 + -1 = 0 0 + t = -1.044030651 + -1 t = -1.044030651 + -1 Combine like terms: -1.044030651 + -1 = -2.044030651 t = -2.044030651 Simplifying t = -2.044030651Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.044030651, -2.044030651}
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