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Simplifying 4.9t2 + -1(4.2104 * 0.966t) + -0.28 = 0 Multiply 4.2104 * 0.966 4.9t2 + -1(4.0672464t) + -0.28 = 0 Remove parenthesis around (4.0672464t) 4.9t2 + -1 * 4.0672464t + -0.28 = 0 Multiply -1 * 4.0672464 4.9t2 + -4.0672464t + -0.28 = 0 Reorder the terms: -0.28 + -4.0672464t + 4.9t2 = 0 Solving -0.28 + -4.0672464t + 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 + -0.8300502857t + t2 = 0 Move the constant term to the right: Add '0.05714285714' to each side of the equation. -0.05714285714 + -0.8300502857t + 0.05714285714 + t2 = 0 + 0.05714285714 Reorder the terms: -0.05714285714 + 0.05714285714 + -0.8300502857t + t2 = 0 + 0.05714285714 Combine like terms: -0.05714285714 + 0.05714285714 = 0.00000000000 0.00000000000 + -0.8300502857t + t2 = 0 + 0.05714285714 -0.8300502857t + t2 = 0 + 0.05714285714 Combine like terms: 0 + 0.05714285714 = 0.05714285714 -0.8300502857t + t2 = 0.05714285714 The t term is -0.8300502857t. Take half its coefficient (-0.4150251429). Square it (0.1722458692) and add it to both sides. Add '0.1722458692' to each side of the equation. -0.8300502857t + 0.1722458692 + t2 = 0.05714285714 + 0.1722458692 Reorder the terms: 0.1722458692 + -0.8300502857t + t2 = 0.05714285714 + 0.1722458692 Combine like terms: 0.05714285714 + 0.1722458692 = 0.22938872634 0.1722458692 + -0.8300502857t + t2 = 0.22938872634 Factor a perfect square on the left side: (t + -0.4150251429)(t + -0.4150251429) = 0.22938872634 Calculate the square root of the right side: 0.478945431 Break this problem into two subproblems by setting (t + -0.4150251429) equal to 0.478945431 and -0.478945431.Subproblem 1
t + -0.4150251429 = 0.478945431 Simplifying t + -0.4150251429 = 0.478945431 Reorder the terms: -0.4150251429 + t = 0.478945431 Solving -0.4150251429 + t = 0.478945431 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.4150251429' to each side of the equation. -0.4150251429 + 0.4150251429 + t = 0.478945431 + 0.4150251429 Combine like terms: -0.4150251429 + 0.4150251429 = 0.0000000000 0.0000000000 + t = 0.478945431 + 0.4150251429 t = 0.478945431 + 0.4150251429 Combine like terms: 0.478945431 + 0.4150251429 = 0.8939705739 t = 0.8939705739 Simplifying t = 0.8939705739Subproblem 2
t + -0.4150251429 = -0.478945431 Simplifying t + -0.4150251429 = -0.478945431 Reorder the terms: -0.4150251429 + t = -0.478945431 Solving -0.4150251429 + t = -0.478945431 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.4150251429' to each side of the equation. -0.4150251429 + 0.4150251429 + t = -0.478945431 + 0.4150251429 Combine like terms: -0.4150251429 + 0.4150251429 = 0.0000000000 0.0000000000 + t = -0.478945431 + 0.4150251429 t = -0.478945431 + 0.4150251429 Combine like terms: -0.478945431 + 0.4150251429 = -0.0639202881 t = -0.0639202881 Simplifying t = -0.0639202881Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.8939705739, -0.0639202881}
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