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Simplifying -0.2t2 + 16t + -28 = 0 Reorder the terms: -28 + 16t + -0.2t2 = 0 Solving -28 + 16t + -0.2t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -0.2 the coefficient of the squared term: Divide each side by '-0.2'. 140 + -80t + t2 = 0 Move the constant term to the right: Add '-140' to each side of the equation. 140 + -80t + -140 + t2 = 0 + -140 Reorder the terms: 140 + -140 + -80t + t2 = 0 + -140 Combine like terms: 140 + -140 = 0 0 + -80t + t2 = 0 + -140 -80t + t2 = 0 + -140 Combine like terms: 0 + -140 = -140 -80t + t2 = -140 The t term is -80t. Take half its coefficient (-40). Square it (1600) and add it to both sides. Add '1600' to each side of the equation. -80t + 1600 + t2 = -140 + 1600 Reorder the terms: 1600 + -80t + t2 = -140 + 1600 Combine like terms: -140 + 1600 = 1460 1600 + -80t + t2 = 1460 Factor a perfect square on the left side: (t + -40)(t + -40) = 1460 Calculate the square root of the right side: 38.209946349 Break this problem into two subproblems by setting (t + -40) equal to 38.209946349 and -38.209946349.Subproblem 1
t + -40 = 38.209946349 Simplifying t + -40 = 38.209946349 Reorder the terms: -40 + t = 38.209946349 Solving -40 + t = 38.209946349 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '40' to each side of the equation. -40 + 40 + t = 38.209946349 + 40 Combine like terms: -40 + 40 = 0 0 + t = 38.209946349 + 40 t = 38.209946349 + 40 Combine like terms: 38.209946349 + 40 = 78.209946349 t = 78.209946349 Simplifying t = 78.209946349Subproblem 2
t + -40 = -38.209946349 Simplifying t + -40 = -38.209946349 Reorder the terms: -40 + t = -38.209946349 Solving -40 + t = -38.209946349 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '40' to each side of the equation. -40 + 40 + t = -38.209946349 + 40 Combine like terms: -40 + 40 = 0 0 + t = -38.209946349 + 40 t = -38.209946349 + 40 Combine like terms: -38.209946349 + 40 = 1.790053651 t = 1.790053651 Simplifying t = 1.790053651Solution
The solution to the problem is based on the solutions from the subproblems. t = {78.209946349, 1.790053651}
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