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Simplifying 2t2 + -64t + 45 = 0 Reorder the terms: 45 + -64t + 2t2 = 0 Solving 45 + -64t + 2t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 22.5 + -32t + t2 = 0 Move the constant term to the right: Add '-22.5' to each side of the equation. 22.5 + -32t + -22.5 + t2 = 0 + -22.5 Reorder the terms: 22.5 + -22.5 + -32t + t2 = 0 + -22.5 Combine like terms: 22.5 + -22.5 = 0.0 0.0 + -32t + t2 = 0 + -22.5 -32t + t2 = 0 + -22.5 Combine like terms: 0 + -22.5 = -22.5 -32t + t2 = -22.5 The t term is -32t. Take half its coefficient (-16). Square it (256) and add it to both sides. Add '256' to each side of the equation. -32t + 256 + t2 = -22.5 + 256 Reorder the terms: 256 + -32t + t2 = -22.5 + 256 Combine like terms: -22.5 + 256 = 233.5 256 + -32t + t2 = 233.5 Factor a perfect square on the left side: (t + -16)(t + -16) = 233.5 Calculate the square root of the right side: 15.28070679 Break this problem into two subproblems by setting (t + -16) equal to 15.28070679 and -15.28070679.Subproblem 1
t + -16 = 15.28070679 Simplifying t + -16 = 15.28070679 Reorder the terms: -16 + t = 15.28070679 Solving -16 + t = 15.28070679 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + t = 15.28070679 + 16 Combine like terms: -16 + 16 = 0 0 + t = 15.28070679 + 16 t = 15.28070679 + 16 Combine like terms: 15.28070679 + 16 = 31.28070679 t = 31.28070679 Simplifying t = 31.28070679Subproblem 2
t + -16 = -15.28070679 Simplifying t + -16 = -15.28070679 Reorder the terms: -16 + t = -15.28070679 Solving -16 + t = -15.28070679 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + t = -15.28070679 + 16 Combine like terms: -16 + 16 = 0 0 + t = -15.28070679 + 16 t = -15.28070679 + 16 Combine like terms: -15.28070679 + 16 = 0.71929321 t = 0.71929321 Simplifying t = 0.71929321Solution
The solution to the problem is based on the solutions from the subproblems. t = {31.28070679, 0.71929321}
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