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Simplifying 4.9t2 + -1(4.87 * 0.259t) + -0.28 = 0 Multiply 4.87 * 0.259 4.9t2 + -1(1.26133t) + -0.28 = 0 Remove parenthesis around (1.26133t) 4.9t2 + -1 * 1.26133t + -0.28 = 0 Multiply -1 * 1.26133 4.9t2 + -1.26133t + -0.28 = 0 Reorder the terms: -0.28 + -1.26133t + 4.9t2 = 0 Solving -0.28 + -1.26133t + 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 + -0.2574142857t + t2 = 0 Move the constant term to the right: Add '0.05714285714' to each side of the equation. -0.05714285714 + -0.2574142857t + 0.05714285714 + t2 = 0 + 0.05714285714 Reorder the terms: -0.05714285714 + 0.05714285714 + -0.2574142857t + t2 = 0 + 0.05714285714 Combine like terms: -0.05714285714 + 0.05714285714 = 0.00000000000 0.00000000000 + -0.2574142857t + t2 = 0 + 0.05714285714 -0.2574142857t + t2 = 0 + 0.05714285714 Combine like terms: 0 + 0.05714285714 = 0.05714285714 -0.2574142857t + t2 = 0.05714285714 The t term is -0.2574142857t. Take half its coefficient (-0.1287071429). Square it (0.01656552863) and add it to both sides. Add '0.01656552863' to each side of the equation. -0.2574142857t + 0.01656552863 + t2 = 0.05714285714 + 0.01656552863 Reorder the terms: 0.01656552863 + -0.2574142857t + t2 = 0.05714285714 + 0.01656552863 Combine like terms: 0.05714285714 + 0.01656552863 = 0.07370838577 0.01656552863 + -0.2574142857t + t2 = 0.07370838577 Factor a perfect square on the left side: (t + -0.1287071429)(t + -0.1287071429) = 0.07370838577 Calculate the square root of the right side: 0.271492883 Break this problem into two subproblems by setting (t + -0.1287071429) equal to 0.271492883 and -0.271492883.Subproblem 1
t + -0.1287071429 = 0.271492883 Simplifying t + -0.1287071429 = 0.271492883 Reorder the terms: -0.1287071429 + t = 0.271492883 Solving -0.1287071429 + t = 0.271492883 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.1287071429' to each side of the equation. -0.1287071429 + 0.1287071429 + t = 0.271492883 + 0.1287071429 Combine like terms: -0.1287071429 + 0.1287071429 = 0.0000000000 0.0000000000 + t = 0.271492883 + 0.1287071429 t = 0.271492883 + 0.1287071429 Combine like terms: 0.271492883 + 0.1287071429 = 0.4002000259 t = 0.4002000259 Simplifying t = 0.4002000259Subproblem 2
t + -0.1287071429 = -0.271492883 Simplifying t + -0.1287071429 = -0.271492883 Reorder the terms: -0.1287071429 + t = -0.271492883 Solving -0.1287071429 + t = -0.271492883 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.1287071429' to each side of the equation. -0.1287071429 + 0.1287071429 + t = -0.271492883 + 0.1287071429 Combine like terms: -0.1287071429 + 0.1287071429 = 0.0000000000 0.0000000000 + t = -0.271492883 + 0.1287071429 t = -0.271492883 + 0.1287071429 Combine like terms: -0.271492883 + 0.1287071429 = -0.1427857401 t = -0.1427857401 Simplifying t = -0.1427857401Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.4002000259, -0.1427857401}
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