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Simplifying -16t2 + 4t + 32.8 = 0 Reorder the terms: 32.8 + 4t + -16t2 = 0 Solving 32.8 + 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'. -2.05 + -0.25t + t2 = 0 Move the constant term to the right: Add '2.05' to each side of the equation. -2.05 + -0.25t + 2.05 + t2 = 0 + 2.05 Reorder the terms: -2.05 + 2.05 + -0.25t + t2 = 0 + 2.05 Combine like terms: -2.05 + 2.05 = 0.00 0.00 + -0.25t + t2 = 0 + 2.05 -0.25t + t2 = 0 + 2.05 Combine like terms: 0 + 2.05 = 2.05 -0.25t + t2 = 2.05 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 = 2.05 + 0.015625 Reorder the terms: 0.015625 + -0.25t + t2 = 2.05 + 0.015625 Combine like terms: 2.05 + 0.015625 = 2.065625 0.015625 + -0.25t + t2 = 2.065625 Factor a perfect square on the left side: (t + -0.125)(t + -0.125) = 2.065625 Calculate the square root of the right side: 1.437228235 Break this problem into two subproblems by setting (t + -0.125) equal to 1.437228235 and -1.437228235.Subproblem 1
t + -0.125 = 1.437228235 Simplifying t + -0.125 = 1.437228235 Reorder the terms: -0.125 + t = 1.437228235 Solving -0.125 + t = 1.437228235 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 = 1.437228235 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + t = 1.437228235 + 0.125 t = 1.437228235 + 0.125 Combine like terms: 1.437228235 + 0.125 = 1.562228235 t = 1.562228235 Simplifying t = 1.562228235Subproblem 2
t + -0.125 = -1.437228235 Simplifying t + -0.125 = -1.437228235 Reorder the terms: -0.125 + t = -1.437228235 Solving -0.125 + t = -1.437228235 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 = -1.437228235 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + t = -1.437228235 + 0.125 t = -1.437228235 + 0.125 Combine like terms: -1.437228235 + 0.125 = -1.312228235 t = -1.312228235 Simplifying t = -1.312228235Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.562228235, -1.312228235}
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