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Simplifying 0 = -16t2 + 45t + 220 Reorder the terms: 0 = 220 + 45t + -16t2 Solving 0 = 220 + 45t + -16t2 Solving for variable 't'. Combine like terms: 0 + -220 = -220 -220 + -45t + 16t2 = 220 + 45t + -16t2 + -220 + -45t + 16t2 Reorder the terms: -220 + -45t + 16t2 = 220 + -220 + 45t + -45t + -16t2 + 16t2 Combine like terms: 220 + -220 = 0 -220 + -45t + 16t2 = 0 + 45t + -45t + -16t2 + 16t2 -220 + -45t + 16t2 = 45t + -45t + -16t2 + 16t2 Combine like terms: 45t + -45t = 0 -220 + -45t + 16t2 = 0 + -16t2 + 16t2 -220 + -45t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -220 + -45t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -13.75 + -2.8125t + t2 = 0 Move the constant term to the right: Add '13.75' to each side of the equation. -13.75 + -2.8125t + 13.75 + t2 = 0 + 13.75 Reorder the terms: -13.75 + 13.75 + -2.8125t + t2 = 0 + 13.75 Combine like terms: -13.75 + 13.75 = 0.00 0.00 + -2.8125t + t2 = 0 + 13.75 -2.8125t + t2 = 0 + 13.75 Combine like terms: 0 + 13.75 = 13.75 -2.8125t + t2 = 13.75 The t term is -2.8125t. Take half its coefficient (-1.40625). Square it (1.977539063) and add it to both sides. Add '1.977539063' to each side of the equation. -2.8125t + 1.977539063 + t2 = 13.75 + 1.977539063 Reorder the terms: 1.977539063 + -2.8125t + t2 = 13.75 + 1.977539063 Combine like terms: 13.75 + 1.977539063 = 15.727539063 1.977539063 + -2.8125t + t2 = 15.727539063 Factor a perfect square on the left side: (t + -1.40625)(t + -1.40625) = 15.727539063 Calculate the square root of the right side: 3.965796145 Break this problem into two subproblems by setting (t + -1.40625) equal to 3.965796145 and -3.965796145.Subproblem 1
t + -1.40625 = 3.965796145 Simplifying t + -1.40625 = 3.965796145 Reorder the terms: -1.40625 + t = 3.965796145 Solving -1.40625 + t = 3.965796145 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.40625' to each side of the equation. -1.40625 + 1.40625 + t = 3.965796145 + 1.40625 Combine like terms: -1.40625 + 1.40625 = 0.00000 0.00000 + t = 3.965796145 + 1.40625 t = 3.965796145 + 1.40625 Combine like terms: 3.965796145 + 1.40625 = 5.372046145 t = 5.372046145 Simplifying t = 5.372046145Subproblem 2
t + -1.40625 = -3.965796145 Simplifying t + -1.40625 = -3.965796145 Reorder the terms: -1.40625 + t = -3.965796145 Solving -1.40625 + t = -3.965796145 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.40625' to each side of the equation. -1.40625 + 1.40625 + t = -3.965796145 + 1.40625 Combine like terms: -1.40625 + 1.40625 = 0.00000 0.00000 + t = -3.965796145 + 1.40625 t = -3.965796145 + 1.40625 Combine like terms: -3.965796145 + 1.40625 = -2.559546145 t = -2.559546145 Simplifying t = -2.559546145Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.372046145, -2.559546145}
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