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Simplifying 4.9t2 + -1(4.2104 * 0.707t) + -0.28 = 0 Multiply 4.2104 * 0.707 4.9t2 + -1(2.9767528t) + -0.28 = 0 Remove parenthesis around (2.9767528t) 4.9t2 + -1 * 2.9767528t + -0.28 = 0 Multiply -1 * 2.9767528 4.9t2 + -2.9767528t + -0.28 = 0 Reorder the terms: -0.28 + -2.9767528t + 4.9t2 = 0 Solving -0.28 + -2.9767528t + 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 + -0.6075005714t + t2 = 0 Move the constant term to the right: Add '0.05714285714' to each side of the equation. -0.05714285714 + -0.6075005714t + 0.05714285714 + t2 = 0 + 0.05714285714 Reorder the terms: -0.05714285714 + 0.05714285714 + -0.6075005714t + t2 = 0 + 0.05714285714 Combine like terms: -0.05714285714 + 0.05714285714 = 0.00000000000 0.00000000000 + -0.6075005714t + t2 = 0 + 0.05714285714 -0.6075005714t + t2 = 0 + 0.05714285714 Combine like terms: 0 + 0.05714285714 = 0.05714285714 -0.6075005714t + t2 = 0.05714285714 The t term is -0.6075005714t. Take half its coefficient (-0.3037502857). Square it (0.09226423606) and add it to both sides. Add '0.09226423606' to each side of the equation. -0.6075005714t + 0.09226423606 + t2 = 0.05714285714 + 0.09226423606 Reorder the terms: 0.09226423606 + -0.6075005714t + t2 = 0.05714285714 + 0.09226423606 Combine like terms: 0.05714285714 + 0.09226423606 = 0.1494070932 0.09226423606 + -0.6075005714t + t2 = 0.1494070932 Factor a perfect square on the left side: (t + -0.3037502857)(t + -0.3037502857) = 0.1494070932 Calculate the square root of the right side: 0.386532137 Break this problem into two subproblems by setting (t + -0.3037502857) equal to 0.386532137 and -0.386532137.Subproblem 1
t + -0.3037502857 = 0.386532137 Simplifying t + -0.3037502857 = 0.386532137 Reorder the terms: -0.3037502857 + t = 0.386532137 Solving -0.3037502857 + t = 0.386532137 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.3037502857' to each side of the equation. -0.3037502857 + 0.3037502857 + t = 0.386532137 + 0.3037502857 Combine like terms: -0.3037502857 + 0.3037502857 = 0.0000000000 0.0000000000 + t = 0.386532137 + 0.3037502857 t = 0.386532137 + 0.3037502857 Combine like terms: 0.386532137 + 0.3037502857 = 0.6902824227 t = 0.6902824227 Simplifying t = 0.6902824227Subproblem 2
t + -0.3037502857 = -0.386532137 Simplifying t + -0.3037502857 = -0.386532137 Reorder the terms: -0.3037502857 + t = -0.386532137 Solving -0.3037502857 + t = -0.386532137 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.3037502857' to each side of the equation. -0.3037502857 + 0.3037502857 + t = -0.386532137 + 0.3037502857 Combine like terms: -0.3037502857 + 0.3037502857 = 0.0000000000 0.0000000000 + t = -0.386532137 + 0.3037502857 t = -0.386532137 + 0.3037502857 Combine like terms: -0.386532137 + 0.3037502857 = -0.0827818513 t = -0.0827818513 Simplifying t = -0.0827818513Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.6902824227, -0.0827818513}
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