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Simplifying 16t2 + 4t + -33 = 0 Reorder the terms: -33 + 4t + 16t2 = 0 Solving -33 + 4t + 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'. -2.0625 + 0.25t + t2 = 0 Move the constant term to the right: Add '2.0625' to each side of the equation. -2.0625 + 0.25t + 2.0625 + t2 = 0 + 2.0625 Reorder the terms: -2.0625 + 2.0625 + 0.25t + t2 = 0 + 2.0625 Combine like terms: -2.0625 + 2.0625 = 0.0000 0.0000 + 0.25t + t2 = 0 + 2.0625 0.25t + t2 = 0 + 2.0625 Combine like terms: 0 + 2.0625 = 2.0625 0.25t + t2 = 2.0625 The t term is 0.25t. Take half its coefficient (0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. 0.25t + 0.015625 + t2 = 2.0625 + 0.015625 Reorder the terms: 0.015625 + 0.25t + t2 = 2.0625 + 0.015625 Combine like terms: 2.0625 + 0.015625 = 2.078125 0.015625 + 0.25t + t2 = 2.078125 Factor a perfect square on the left side: (t + 0.125)(t + 0.125) = 2.078125 Calculate the square root of the right side: 1.441570324 Break this problem into two subproblems by setting (t + 0.125) equal to 1.441570324 and -1.441570324.Subproblem 1
t + 0.125 = 1.441570324 Simplifying t + 0.125 = 1.441570324 Reorder the terms: 0.125 + t = 1.441570324 Solving 0.125 + t = 1.441570324 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + t = 1.441570324 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + t = 1.441570324 + -0.125 t = 1.441570324 + -0.125 Combine like terms: 1.441570324 + -0.125 = 1.316570324 t = 1.316570324 Simplifying t = 1.316570324Subproblem 2
t + 0.125 = -1.441570324 Simplifying t + 0.125 = -1.441570324 Reorder the terms: 0.125 + t = -1.441570324 Solving 0.125 + t = -1.441570324 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + t = -1.441570324 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + t = -1.441570324 + -0.125 t = -1.441570324 + -0.125 Combine like terms: -1.441570324 + -0.125 = -1.566570324 t = -1.566570324 Simplifying t = -1.566570324Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.316570324, -1.566570324}
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