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Simplifying 4.9t2 + -0.2977t + -0.28 = 0 Reorder the terms: -0.28 + -0.2977t + 4.9t2 = 0 Solving -0.28 + -0.2977t + 4.9t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -0.05714285714 + -0.06075510204t + t2 = 0 Move the constant term to the right: Add '0.05714285714' to each side of the equation. -0.05714285714 + -0.06075510204t + 0.05714285714 + t2 = 0 + 0.05714285714 Reorder the terms: -0.05714285714 + 0.05714285714 + -0.06075510204t + t2 = 0 + 0.05714285714 Combine like terms: -0.05714285714 + 0.05714285714 = 0.00000000000 0.00000000000 + -0.06075510204t + t2 = 0 + 0.05714285714 -0.06075510204t + t2 = 0 + 0.05714285714 Combine like terms: 0 + 0.05714285714 = 0.05714285714 -0.06075510204t + t2 = 0.05714285714 The t term is -0.06075510204t. Take half its coefficient (-0.03037755102). Square it (0.0009227956060) and add it to both sides. Add '0.0009227956060' to each side of the equation. -0.06075510204t + 0.0009227956060 + t2 = 0.05714285714 + 0.0009227956060 Reorder the terms: 0.0009227956060 + -0.06075510204t + t2 = 0.05714285714 + 0.0009227956060 Combine like terms: 0.05714285714 + 0.0009227956060 = 0.058065652746 0.0009227956060 + -0.06075510204t + t2 = 0.058065652746 Factor a perfect square on the left side: (t + -0.03037755102)(t + -0.03037755102) = 0.058065652746 Calculate the square root of the right side: 0.240968157 Break this problem into two subproblems by setting (t + -0.03037755102) equal to 0.240968157 and -0.240968157.Subproblem 1
t + -0.03037755102 = 0.240968157 Simplifying t + -0.03037755102 = 0.240968157 Reorder the terms: -0.03037755102 + t = 0.240968157 Solving -0.03037755102 + t = 0.240968157 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.03037755102' to each side of the equation. -0.03037755102 + 0.03037755102 + t = 0.240968157 + 0.03037755102 Combine like terms: -0.03037755102 + 0.03037755102 = 0.00000000000 0.00000000000 + t = 0.240968157 + 0.03037755102 t = 0.240968157 + 0.03037755102 Combine like terms: 0.240968157 + 0.03037755102 = 0.27134570802 t = 0.27134570802 Simplifying t = 0.27134570802Subproblem 2
t + -0.03037755102 = -0.240968157 Simplifying t + -0.03037755102 = -0.240968157 Reorder the terms: -0.03037755102 + t = -0.240968157 Solving -0.03037755102 + t = -0.240968157 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.03037755102' to each side of the equation. -0.03037755102 + 0.03037755102 + t = -0.240968157 + 0.03037755102 Combine like terms: -0.03037755102 + 0.03037755102 = 0.00000000000 0.00000000000 + t = -0.240968157 + 0.03037755102 t = -0.240968157 + 0.03037755102 Combine like terms: -0.240968157 + 0.03037755102 = -0.21059060598 t = -0.21059060598 Simplifying t = -0.21059060598Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.27134570802, -0.21059060598}
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