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Simplifying 16t2 + 25t + 5 = 0 Reorder the terms: 5 + 25t + 16t2 = 0 Solving 5 + 25t + 16t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 0.3125 + 1.5625t + t2 = 0 Move the constant term to the right: Add '-0.3125' to each side of the equation. 0.3125 + 1.5625t + -0.3125 + t2 = 0 + -0.3125 Reorder the terms: 0.3125 + -0.3125 + 1.5625t + t2 = 0 + -0.3125 Combine like terms: 0.3125 + -0.3125 = 0.0000 0.0000 + 1.5625t + t2 = 0 + -0.3125 1.5625t + t2 = 0 + -0.3125 Combine like terms: 0 + -0.3125 = -0.3125 1.5625t + t2 = -0.3125 The t term is 1.5625t. Take half its coefficient (0.78125). Square it (0.6103515625) and add it to both sides. Add '0.6103515625' to each side of the equation. 1.5625t + 0.6103515625 + t2 = -0.3125 + 0.6103515625 Reorder the terms: 0.6103515625 + 1.5625t + t2 = -0.3125 + 0.6103515625 Combine like terms: -0.3125 + 0.6103515625 = 0.2978515625 0.6103515625 + 1.5625t + t2 = 0.2978515625 Factor a perfect square on the left side: (t + 0.78125)(t + 0.78125) = 0.2978515625 Calculate the square root of the right side: 0.545757787 Break this problem into two subproblems by setting (t + 0.78125) equal to 0.545757787 and -0.545757787.Subproblem 1
t + 0.78125 = 0.545757787 Simplifying t + 0.78125 = 0.545757787 Reorder the terms: 0.78125 + t = 0.545757787 Solving 0.78125 + t = 0.545757787 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.78125' to each side of the equation. 0.78125 + -0.78125 + t = 0.545757787 + -0.78125 Combine like terms: 0.78125 + -0.78125 = 0.00000 0.00000 + t = 0.545757787 + -0.78125 t = 0.545757787 + -0.78125 Combine like terms: 0.545757787 + -0.78125 = -0.235492213 t = -0.235492213 Simplifying t = -0.235492213Subproblem 2
t + 0.78125 = -0.545757787 Simplifying t + 0.78125 = -0.545757787 Reorder the terms: 0.78125 + t = -0.545757787 Solving 0.78125 + t = -0.545757787 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.78125' to each side of the equation. 0.78125 + -0.78125 + t = -0.545757787 + -0.78125 Combine like terms: 0.78125 + -0.78125 = 0.00000 0.00000 + t = -0.545757787 + -0.78125 t = -0.545757787 + -0.78125 Combine like terms: -0.545757787 + -0.78125 = -1.327007787 t = -1.327007787 Simplifying t = -1.327007787Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.235492213, -1.327007787}
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