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Simplifying 4.905t2 + 2t = 100 Reorder the terms: 2t + 4.905t2 = 100 Solving 2t + 4.905t2 = 100 Solving for variable 't'. Reorder the terms: -100 + 2t + 4.905t2 = 100 + -100 Combine like terms: 100 + -100 = 0 -100 + 2t + 4.905t2 = 0 Begin completing the square. Divide all terms by 4.905 the coefficient of the squared term: Divide each side by '4.905'. -20.38735984 + 0.4077471967t + t2 = 0 Move the constant term to the right: Add '20.38735984' to each side of the equation. -20.38735984 + 0.4077471967t + 20.38735984 + t2 = 0 + 20.38735984 Reorder the terms: -20.38735984 + 20.38735984 + 0.4077471967t + t2 = 0 + 20.38735984 Combine like terms: -20.38735984 + 20.38735984 = 0.00000000 0.00000000 + 0.4077471967t + t2 = 0 + 20.38735984 0.4077471967t + t2 = 0 + 20.38735984 Combine like terms: 0 + 20.38735984 = 20.38735984 0.4077471967t + t2 = 20.38735984 The t term is 0.4077471967t. Take half its coefficient (0.2038735984). Square it (0.04156444412) and add it to both sides. Add '0.04156444412' to each side of the equation. 0.4077471967t + 0.04156444412 + t2 = 20.38735984 + 0.04156444412 Reorder the terms: 0.04156444412 + 0.4077471967t + t2 = 20.38735984 + 0.04156444412 Combine like terms: 20.38735984 + 0.04156444412 = 20.42892428412 0.04156444412 + 0.4077471967t + t2 = 20.42892428412 Factor a perfect square on the left side: (t + 0.2038735984)(t + 0.2038735984) = 20.42892428412 Calculate the square root of the right side: 4.519836754 Break this problem into two subproblems by setting (t + 0.2038735984) equal to 4.519836754 and -4.519836754.Subproblem 1
t + 0.2038735984 = 4.519836754 Simplifying t + 0.2038735984 = 4.519836754 Reorder the terms: 0.2038735984 + t = 4.519836754 Solving 0.2038735984 + t = 4.519836754 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.2038735984' to each side of the equation. 0.2038735984 + -0.2038735984 + t = 4.519836754 + -0.2038735984 Combine like terms: 0.2038735984 + -0.2038735984 = 0.0000000000 0.0000000000 + t = 4.519836754 + -0.2038735984 t = 4.519836754 + -0.2038735984 Combine like terms: 4.519836754 + -0.2038735984 = 4.3159631556 t = 4.3159631556 Simplifying t = 4.3159631556Subproblem 2
t + 0.2038735984 = -4.519836754 Simplifying t + 0.2038735984 = -4.519836754 Reorder the terms: 0.2038735984 + t = -4.519836754 Solving 0.2038735984 + t = -4.519836754 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.2038735984' to each side of the equation. 0.2038735984 + -0.2038735984 + t = -4.519836754 + -0.2038735984 Combine like terms: 0.2038735984 + -0.2038735984 = 0.0000000000 0.0000000000 + t = -4.519836754 + -0.2038735984 t = -4.519836754 + -0.2038735984 Combine like terms: -4.519836754 + -0.2038735984 = -4.7237103524 t = -4.7237103524 Simplifying t = -4.7237103524Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.3159631556, -4.7237103524}
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