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Simplifying 4.9t2 + -6.79t + 0.65 = 0 Reorder the terms: 0.65 + -6.79t + 4.9t2 = 0 Solving 0.65 + -6.79t + 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'. 0.1326530612 + -1.385714286t + t2 = 0 Move the constant term to the right: Add '-0.1326530612' to each side of the equation. 0.1326530612 + -1.385714286t + -0.1326530612 + t2 = 0 + -0.1326530612 Reorder the terms: 0.1326530612 + -0.1326530612 + -1.385714286t + t2 = 0 + -0.1326530612 Combine like terms: 0.1326530612 + -0.1326530612 = 0.0000000000 0.0000000000 + -1.385714286t + t2 = 0 + -0.1326530612 -1.385714286t + t2 = 0 + -0.1326530612 Combine like terms: 0 + -0.1326530612 = -0.1326530612 -1.385714286t + t2 = -0.1326530612 The t term is -1.385714286t. Take half its coefficient (-0.692857143). Square it (0.4800510206) and add it to both sides. Add '0.4800510206' to each side of the equation. -1.385714286t + 0.4800510206 + t2 = -0.1326530612 + 0.4800510206 Reorder the terms: 0.4800510206 + -1.385714286t + t2 = -0.1326530612 + 0.4800510206 Combine like terms: -0.1326530612 + 0.4800510206 = 0.3473979594 0.4800510206 + -1.385714286t + t2 = 0.3473979594 Factor a perfect square on the left side: (t + -0.692857143)(t + -0.692857143) = 0.3473979594 Calculate the square root of the right side: 0.58940475 Break this problem into two subproblems by setting (t + -0.692857143) equal to 0.58940475 and -0.58940475.Subproblem 1
t + -0.692857143 = 0.58940475 Simplifying t + -0.692857143 = 0.58940475 Reorder the terms: -0.692857143 + t = 0.58940475 Solving -0.692857143 + t = 0.58940475 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.692857143' to each side of the equation. -0.692857143 + 0.692857143 + t = 0.58940475 + 0.692857143 Combine like terms: -0.692857143 + 0.692857143 = 0.000000000 0.000000000 + t = 0.58940475 + 0.692857143 t = 0.58940475 + 0.692857143 Combine like terms: 0.58940475 + 0.692857143 = 1.282261893 t = 1.282261893 Simplifying t = 1.282261893Subproblem 2
t + -0.692857143 = -0.58940475 Simplifying t + -0.692857143 = -0.58940475 Reorder the terms: -0.692857143 + t = -0.58940475 Solving -0.692857143 + t = -0.58940475 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.692857143' to each side of the equation. -0.692857143 + 0.692857143 + t = -0.58940475 + 0.692857143 Combine like terms: -0.692857143 + 0.692857143 = 0.000000000 0.000000000 + t = -0.58940475 + 0.692857143 t = -0.58940475 + 0.692857143 Combine like terms: -0.58940475 + 0.692857143 = 0.103452393 t = 0.103452393 Simplifying t = 0.103452393Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.282261893, 0.103452393}
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