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Simplifying 0.1t2 + -20t + 888.8 = 0 Reorder the terms: 888.8 + -20t + 0.1t2 = 0 Solving 888.8 + -20t + 0.1t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 0.1 the coefficient of the squared term: Divide each side by '0.1'. 8888 + -200t + t2 = 0 Move the constant term to the right: Add '-8888' to each side of the equation. 8888 + -200t + -8888 + t2 = 0 + -8888 Reorder the terms: 8888 + -8888 + -200t + t2 = 0 + -8888 Combine like terms: 8888 + -8888 = 0 0 + -200t + t2 = 0 + -8888 -200t + t2 = 0 + -8888 Combine like terms: 0 + -8888 = -8888 -200t + t2 = -8888 The t term is -200t. Take half its coefficient (-100). Square it (10000) and add it to both sides. Add '10000' to each side of the equation. -200t + 10000 + t2 = -8888 + 10000 Reorder the terms: 10000 + -200t + t2 = -8888 + 10000 Combine like terms: -8888 + 10000 = 1112 10000 + -200t + t2 = 1112 Factor a perfect square on the left side: (t + -100)(t + -100) = 1112 Calculate the square root of the right side: 33.346664001 Break this problem into two subproblems by setting (t + -100) equal to 33.346664001 and -33.346664001.Subproblem 1
t + -100 = 33.346664001 Simplifying t + -100 = 33.346664001 Reorder the terms: -100 + t = 33.346664001 Solving -100 + t = 33.346664001 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '100' to each side of the equation. -100 + 100 + t = 33.346664001 + 100 Combine like terms: -100 + 100 = 0 0 + t = 33.346664001 + 100 t = 33.346664001 + 100 Combine like terms: 33.346664001 + 100 = 133.346664001 t = 133.346664001 Simplifying t = 133.346664001Subproblem 2
t + -100 = -33.346664001 Simplifying t + -100 = -33.346664001 Reorder the terms: -100 + t = -33.346664001 Solving -100 + t = -33.346664001 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '100' to each side of the equation. -100 + 100 + t = -33.346664001 + 100 Combine like terms: -100 + 100 = 0 0 + t = -33.346664001 + 100 t = -33.346664001 + 100 Combine like terms: -33.346664001 + 100 = 66.653335999 t = 66.653335999 Simplifying t = 66.653335999Solution
The solution to the problem is based on the solutions from the subproblems. t = {133.346664001, 66.653335999}
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