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Simplifying 40 = 20t + t2 Solving 40 = 20t + t2 Solving for variable 't'. Reorder the terms: 40 + -20t + -1t2 = 20t + -20t + t2 + -1t2 Combine like terms: 20t + -20t = 0 40 + -20t + -1t2 = 0 + t2 + -1t2 40 + -20t + -1t2 = t2 + -1t2 Combine like terms: t2 + -1t2 = 0 40 + -20t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -40 + 20t + t2 = 0 Move the constant term to the right: Add '40' to each side of the equation. -40 + 20t + 40 + t2 = 0 + 40 Reorder the terms: -40 + 40 + 20t + t2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + 20t + t2 = 0 + 40 20t + t2 = 0 + 40 Combine like terms: 0 + 40 = 40 20t + t2 = 40 The t term is 20t. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20t + 100 + t2 = 40 + 100 Reorder the terms: 100 + 20t + t2 = 40 + 100 Combine like terms: 40 + 100 = 140 100 + 20t + t2 = 140 Factor a perfect square on the left side: (t + 10)(t + 10) = 140 Calculate the square root of the right side: 11.832159566 Break this problem into two subproblems by setting (t + 10) equal to 11.832159566 and -11.832159566.Subproblem 1
t + 10 = 11.832159566 Simplifying t + 10 = 11.832159566 Reorder the terms: 10 + t = 11.832159566 Solving 10 + t = 11.832159566 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + t = 11.832159566 + -10 Combine like terms: 10 + -10 = 0 0 + t = 11.832159566 + -10 t = 11.832159566 + -10 Combine like terms: 11.832159566 + -10 = 1.832159566 t = 1.832159566 Simplifying t = 1.832159566Subproblem 2
t + 10 = -11.832159566 Simplifying t + 10 = -11.832159566 Reorder the terms: 10 + t = -11.832159566 Solving 10 + t = -11.832159566 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + t = -11.832159566 + -10 Combine like terms: 10 + -10 = 0 0 + t = -11.832159566 + -10 t = -11.832159566 + -10 Combine like terms: -11.832159566 + -10 = -21.832159566 t = -21.832159566 Simplifying t = -21.832159566Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.832159566, -21.832159566}
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