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Simplifying (1.75t2) + 4.17t + -25 = 0 Reorder the terms: -25 + 4.17t + (1.75t2) = 0 Solving -25 + 4.17t + (1.75t2) = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 1.75 the coefficient of the squared term: Divide each side by '1.75'. -14.28571429 + 2.382857143t + t2 = 0 Move the constant term to the right: Add '14.28571429' to each side of the equation. -14.28571429 + 2.382857143t + 14.28571429 + t2 = 0 + 14.28571429 Reorder the terms: -14.28571429 + 14.28571429 + 2.382857143t + t2 = 0 + 14.28571429 Combine like terms: -14.28571429 + 14.28571429 = 0.00000000 0.00000000 + 2.382857143t + t2 = 0 + 14.28571429 2.382857143t + t2 = 0 + 14.28571429 Combine like terms: 0 + 14.28571429 = 14.28571429 2.382857143t + t2 = 14.28571429 The t term is 2.382857143t. Take half its coefficient (1.191428572). Square it (1.419502042) and add it to both sides. Add '1.419502042' to each side of the equation. 2.382857143t + 1.419502042 + t2 = 14.28571429 + 1.419502042 Reorder the terms: 1.419502042 + 2.382857143t + t2 = 14.28571429 + 1.419502042 Combine like terms: 14.28571429 + 1.419502042 = 15.705216332 1.419502042 + 2.382857143t + t2 = 15.705216332 Factor a perfect square on the left side: ((t) + 1.191428572)((t) + 1.191428572) = 15.705216332 Calculate the square root of the right side: 3.962980738 Break this problem into two subproblems by setting ((t) + 1.191428572) equal to 3.962980738 and -3.962980738.Subproblem 1
(t) + 1.191428572 = 3.962980738 Simplifying (t) + 1.191428572 = 3.962980738 t + 1.191428572 = 3.962980738 Reorder the terms: 1.191428572 + t = 3.962980738 Solving 1.191428572 + t = 3.962980738 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.191428572' to each side of the equation. 1.191428572 + -1.191428572 + t = 3.962980738 + -1.191428572 Combine like terms: 1.191428572 + -1.191428572 = 0.000000000 0.000000000 + t = 3.962980738 + -1.191428572 t = 3.962980738 + -1.191428572 Combine like terms: 3.962980738 + -1.191428572 = 2.771552166 t = 2.771552166 Simplifying t = 2.771552166Subproblem 2
(t) + 1.191428572 = -3.962980738 Simplifying (t) + 1.191428572 = -3.962980738 t + 1.191428572 = -3.962980738 Reorder the terms: 1.191428572 + t = -3.962980738 Solving 1.191428572 + t = -3.962980738 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.191428572' to each side of the equation. 1.191428572 + -1.191428572 + t = -3.962980738 + -1.191428572 Combine like terms: 1.191428572 + -1.191428572 = 0.000000000 0.000000000 + t = -3.962980738 + -1.191428572 t = -3.962980738 + -1.191428572 Combine like terms: -3.962980738 + -1.191428572 = -5.15440931 t = -5.15440931 Simplifying t = -5.15440931Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.771552166, -5.15440931}
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