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Simplifying 16t2 + -37t + -20 = 0 Reorder the terms: -20 + -37t + 16t2 = 0 Solving -20 + -37t + 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'. -1.25 + -2.3125t + t2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + -2.3125t + 1.25 + t2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + -2.3125t + t2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + -2.3125t + t2 = 0 + 1.25 -2.3125t + t2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 -2.3125t + t2 = 1.25 The t term is -2.3125t. Take half its coefficient (-1.15625). Square it (1.336914063) and add it to both sides. Add '1.336914063' to each side of the equation. -2.3125t + 1.336914063 + t2 = 1.25 + 1.336914063 Reorder the terms: 1.336914063 + -2.3125t + t2 = 1.25 + 1.336914063 Combine like terms: 1.25 + 1.336914063 = 2.586914063 1.336914063 + -2.3125t + t2 = 2.586914063 Factor a perfect square on the left side: (t + -1.15625)(t + -1.15625) = 2.586914063 Calculate the square root of the right side: 1.608388654 Break this problem into two subproblems by setting (t + -1.15625) equal to 1.608388654 and -1.608388654.Subproblem 1
t + -1.15625 = 1.608388654 Simplifying t + -1.15625 = 1.608388654 Reorder the terms: -1.15625 + t = 1.608388654 Solving -1.15625 + t = 1.608388654 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.15625' to each side of the equation. -1.15625 + 1.15625 + t = 1.608388654 + 1.15625 Combine like terms: -1.15625 + 1.15625 = 0.00000 0.00000 + t = 1.608388654 + 1.15625 t = 1.608388654 + 1.15625 Combine like terms: 1.608388654 + 1.15625 = 2.764638654 t = 2.764638654 Simplifying t = 2.764638654Subproblem 2
t + -1.15625 = -1.608388654 Simplifying t + -1.15625 = -1.608388654 Reorder the terms: -1.15625 + t = -1.608388654 Solving -1.15625 + t = -1.608388654 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.15625' to each side of the equation. -1.15625 + 1.15625 + t = -1.608388654 + 1.15625 Combine like terms: -1.15625 + 1.15625 = 0.00000 0.00000 + t = -1.608388654 + 1.15625 t = -1.608388654 + 1.15625 Combine like terms: -1.608388654 + 1.15625 = -0.452138654 t = -0.452138654 Simplifying t = -0.452138654Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.764638654, -0.452138654}
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