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Simplifying 4.905t2 + -1t + -10 = 0 Reorder the terms: -10 + -1t + 4.905t2 = 0 Solving -10 + -1t + 4.905t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 4.905 the coefficient of the squared term: Divide each side by '4.905'. -2.038735984 + -0.2038735984t + t2 = 0 Move the constant term to the right: Add '2.038735984' to each side of the equation. -2.038735984 + -0.2038735984t + 2.038735984 + t2 = 0 + 2.038735984 Reorder the terms: -2.038735984 + 2.038735984 + -0.2038735984t + t2 = 0 + 2.038735984 Combine like terms: -2.038735984 + 2.038735984 = 0.000000000 0.000000000 + -0.2038735984t + t2 = 0 + 2.038735984 -0.2038735984t + t2 = 0 + 2.038735984 Combine like terms: 0 + 2.038735984 = 2.038735984 -0.2038735984t + t2 = 2.038735984 The t term is -0.2038735984t. Take half its coefficient (-0.1019367992). Square it (0.01039111103) and add it to both sides. Add '0.01039111103' to each side of the equation. -0.2038735984t + 0.01039111103 + t2 = 2.038735984 + 0.01039111103 Reorder the terms: 0.01039111103 + -0.2038735984t + t2 = 2.038735984 + 0.01039111103 Combine like terms: 2.038735984 + 0.01039111103 = 2.04912709503 0.01039111103 + -0.2038735984t + t2 = 2.04912709503 Factor a perfect square on the left side: (t + -0.1019367992)(t + -0.1019367992) = 2.04912709503 Calculate the square root of the right side: 1.431477242 Break this problem into two subproblems by setting (t + -0.1019367992) equal to 1.431477242 and -1.431477242.Subproblem 1
t + -0.1019367992 = 1.431477242 Simplifying t + -0.1019367992 = 1.431477242 Reorder the terms: -0.1019367992 + t = 1.431477242 Solving -0.1019367992 + t = 1.431477242 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.1019367992' to each side of the equation. -0.1019367992 + 0.1019367992 + t = 1.431477242 + 0.1019367992 Combine like terms: -0.1019367992 + 0.1019367992 = 0.0000000000 0.0000000000 + t = 1.431477242 + 0.1019367992 t = 1.431477242 + 0.1019367992 Combine like terms: 1.431477242 + 0.1019367992 = 1.5334140412 t = 1.5334140412 Simplifying t = 1.5334140412Subproblem 2
t + -0.1019367992 = -1.431477242 Simplifying t + -0.1019367992 = -1.431477242 Reorder the terms: -0.1019367992 + t = -1.431477242 Solving -0.1019367992 + t = -1.431477242 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.1019367992' to each side of the equation. -0.1019367992 + 0.1019367992 + t = -1.431477242 + 0.1019367992 Combine like terms: -0.1019367992 + 0.1019367992 = 0.0000000000 0.0000000000 + t = -1.431477242 + 0.1019367992 t = -1.431477242 + 0.1019367992 Combine like terms: -1.431477242 + 0.1019367992 = -1.3295404428 t = -1.3295404428 Simplifying t = -1.3295404428Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.5334140412, -1.3295404428}
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