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Simplifying 0 = 425 + -10t + -1(t2) Solving 0 = 425 + -10t + -1t2 Solving for variable 't'. Combine like terms: 0 + -425 = -425 -425 + 10t + t2 = 425 + -10t + -1t2 + -425 + 10t + t2 Reorder the terms: -425 + 10t + t2 = 425 + -425 + -10t + 10t + -1t2 + t2 Combine like terms: 425 + -425 = 0 -425 + 10t + t2 = 0 + -10t + 10t + -1t2 + t2 -425 + 10t + t2 = -10t + 10t + -1t2 + t2 Combine like terms: -10t + 10t = 0 -425 + 10t + t2 = 0 + -1t2 + t2 -425 + 10t + t2 = -1t2 + t2 Combine like terms: -1t2 + t2 = 0 -425 + 10t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '425' to each side of the equation. -425 + 10t + 425 + t2 = 0 + 425 Reorder the terms: -425 + 425 + 10t + t2 = 0 + 425 Combine like terms: -425 + 425 = 0 0 + 10t + t2 = 0 + 425 10t + t2 = 0 + 425 Combine like terms: 0 + 425 = 425 10t + t2 = 425 The t term is 10t. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10t + 25 + t2 = 425 + 25 Reorder the terms: 25 + 10t + t2 = 425 + 25 Combine like terms: 425 + 25 = 450 25 + 10t + t2 = 450 Factor a perfect square on the left side: (t + 5)(t + 5) = 450 Calculate the square root of the right side: 21.213203436 Break this problem into two subproblems by setting (t + 5) equal to 21.213203436 and -21.213203436.Subproblem 1
t + 5 = 21.213203436 Simplifying t + 5 = 21.213203436 Reorder the terms: 5 + t = 21.213203436 Solving 5 + t = 21.213203436 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + t = 21.213203436 + -5 Combine like terms: 5 + -5 = 0 0 + t = 21.213203436 + -5 t = 21.213203436 + -5 Combine like terms: 21.213203436 + -5 = 16.213203436 t = 16.213203436 Simplifying t = 16.213203436Subproblem 2
t + 5 = -21.213203436 Simplifying t + 5 = -21.213203436 Reorder the terms: 5 + t = -21.213203436 Solving 5 + t = -21.213203436 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + t = -21.213203436 + -5 Combine like terms: 5 + -5 = 0 0 + t = -21.213203436 + -5 t = -21.213203436 + -5 Combine like terms: -21.213203436 + -5 = -26.213203436 t = -26.213203436 Simplifying t = -26.213203436Solution
The solution to the problem is based on the solutions from the subproblems. t = {16.213203436, -26.213203436}
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