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Simplifying (5t * t) + -1(11t) + -8400 = 0 Multiply t * t (5t2) + -1(11t) + -8400 = 0 Remove parenthesis around (11t) (5t2) + -1 * 11t + -8400 = 0 Multiply -1 * 11 (5t2) + -11t + -8400 = 0 Reorder the terms: -8400 + -11t + (5t2) = 0 Solving -8400 + -11t + (5t2) = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1680 + -2.2t + t2 = 0 Move the constant term to the right: Add '1680' to each side of the equation. -1680 + -2.2t + 1680 + t2 = 0 + 1680 Reorder the terms: -1680 + 1680 + -2.2t + t2 = 0 + 1680 Combine like terms: -1680 + 1680 = 0 0 + -2.2t + t2 = 0 + 1680 -2.2t + t2 = 0 + 1680 Combine like terms: 0 + 1680 = 1680 -2.2t + t2 = 1680 The t term is -2.2t. Take half its coefficient (-1.1). Square it (1.21) and add it to both sides. Add '1.21' to each side of the equation. -2.2t + 1.21 + t2 = 1680 + 1.21 Reorder the terms: 1.21 + -2.2t + t2 = 1680 + 1.21 Combine like terms: 1680 + 1.21 = 1681.21 1.21 + -2.2t + t2 = 1681.21 Factor a perfect square on the left side: ((t) + -1.1)((t) + -1.1) = 1681.21 Calculate the square root of the right side: 41.002560896 Break this problem into two subproblems by setting ((t) + -1.1) equal to 41.002560896 and -41.002560896.Subproblem 1
(t) + -1.1 = 41.002560896 Simplifying (t) + -1.1 = 41.002560896 t + -1.1 = 41.002560896 Reorder the terms: -1.1 + t = 41.002560896 Solving -1.1 + t = 41.002560896 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.1' to each side of the equation. -1.1 + 1.1 + t = 41.002560896 + 1.1 Combine like terms: -1.1 + 1.1 = 0.0 0.0 + t = 41.002560896 + 1.1 t = 41.002560896 + 1.1 Combine like terms: 41.002560896 + 1.1 = 42.102560896 t = 42.102560896 Simplifying t = 42.102560896Subproblem 2
(t) + -1.1 = -41.002560896 Simplifying (t) + -1.1 = -41.002560896 t + -1.1 = -41.002560896 Reorder the terms: -1.1 + t = -41.002560896 Solving -1.1 + t = -41.002560896 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.1' to each side of the equation. -1.1 + 1.1 + t = -41.002560896 + 1.1 Combine like terms: -1.1 + 1.1 = 0.0 0.0 + t = -41.002560896 + 1.1 t = -41.002560896 + 1.1 Combine like terms: -41.002560896 + 1.1 = -39.902560896 t = -39.902560896 Simplifying t = -39.902560896Solution
The solution to the problem is based on the solutions from the subproblems. t = {42.102560896, -39.902560896}
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