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Simplifying 0.1t2 = 20t + 10 Reorder the terms: 0.1t2 = 10 + 20t Solving 0.1t2 = 10 + 20t Solving for variable 't'. Reorder the terms: -10 + -20t + 0.1t2 = 10 + 20t + -10 + -20t Reorder the terms: -10 + -20t + 0.1t2 = 10 + -10 + 20t + -20t Combine like terms: 10 + -10 = 0 -10 + -20t + 0.1t2 = 0 + 20t + -20t -10 + -20t + 0.1t2 = 20t + -20t Combine like terms: 20t + -20t = 0 -10 + -20t + 0.1t2 = 0 Begin completing the square. Divide all terms by 0.1 the coefficient of the squared term: Divide each side by '0.1'. -100 + -200t + t2 = 0 Move the constant term to the right: Add '100' to each side of the equation. -100 + -200t + 100 + t2 = 0 + 100 Reorder the terms: -100 + 100 + -200t + t2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + -200t + t2 = 0 + 100 -200t + t2 = 0 + 100 Combine like terms: 0 + 100 = 100 -200t + t2 = 100 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 = 100 + 10000 Reorder the terms: 10000 + -200t + t2 = 100 + 10000 Combine like terms: 100 + 10000 = 10100 10000 + -200t + t2 = 10100 Factor a perfect square on the left side: (t + -100)(t + -100) = 10100 Calculate the square root of the right side: 100.498756211 Break this problem into two subproblems by setting (t + -100) equal to 100.498756211 and -100.498756211.Subproblem 1
t + -100 = 100.498756211 Simplifying t + -100 = 100.498756211 Reorder the terms: -100 + t = 100.498756211 Solving -100 + t = 100.498756211 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 = 100.498756211 + 100 Combine like terms: -100 + 100 = 0 0 + t = 100.498756211 + 100 t = 100.498756211 + 100 Combine like terms: 100.498756211 + 100 = 200.498756211 t = 200.498756211 Simplifying t = 200.498756211Subproblem 2
t + -100 = -100.498756211 Simplifying t + -100 = -100.498756211 Reorder the terms: -100 + t = -100.498756211 Solving -100 + t = -100.498756211 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 = -100.498756211 + 100 Combine like terms: -100 + 100 = 0 0 + t = -100.498756211 + 100 t = -100.498756211 + 100 Combine like terms: -100.498756211 + 100 = -0.498756211 t = -0.498756211 Simplifying t = -0.498756211Solution
The solution to the problem is based on the solutions from the subproblems. t = {200.498756211, -0.498756211}
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