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Simplifying 4.9t2 + -14t + 5 = 0 Reorder the terms: 5 + -14t + 4.9t2 = 0 Solving 5 + -14t + 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'. 1.020408163 + -2.857142857t + t2 = 0 Move the constant term to the right: Add '-1.020408163' to each side of the equation. 1.020408163 + -2.857142857t + -1.020408163 + t2 = 0 + -1.020408163 Reorder the terms: 1.020408163 + -1.020408163 + -2.857142857t + t2 = 0 + -1.020408163 Combine like terms: 1.020408163 + -1.020408163 = 0.000000000 0.000000000 + -2.857142857t + t2 = 0 + -1.020408163 -2.857142857t + t2 = 0 + -1.020408163 Combine like terms: 0 + -1.020408163 = -1.020408163 -2.857142857t + t2 = -1.020408163 The t term is -2.857142857t. Take half its coefficient (-1.428571429). Square it (2.040816328) and add it to both sides. Add '2.040816328' to each side of the equation. -2.857142857t + 2.040816328 + t2 = -1.020408163 + 2.040816328 Reorder the terms: 2.040816328 + -2.857142857t + t2 = -1.020408163 + 2.040816328 Combine like terms: -1.020408163 + 2.040816328 = 1.020408165 2.040816328 + -2.857142857t + t2 = 1.020408165 Factor a perfect square on the left side: (t + -1.428571429)(t + -1.428571429) = 1.020408165 Calculate the square root of the right side: 1.010152545 Break this problem into two subproblems by setting (t + -1.428571429) equal to 1.010152545 and -1.010152545.Subproblem 1
t + -1.428571429 = 1.010152545 Simplifying t + -1.428571429 = 1.010152545 Reorder the terms: -1.428571429 + t = 1.010152545 Solving -1.428571429 + t = 1.010152545 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.428571429' to each side of the equation. -1.428571429 + 1.428571429 + t = 1.010152545 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + t = 1.010152545 + 1.428571429 t = 1.010152545 + 1.428571429 Combine like terms: 1.010152545 + 1.428571429 = 2.438723974 t = 2.438723974 Simplifying t = 2.438723974Subproblem 2
t + -1.428571429 = -1.010152545 Simplifying t + -1.428571429 = -1.010152545 Reorder the terms: -1.428571429 + t = -1.010152545 Solving -1.428571429 + t = -1.010152545 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.428571429' to each side of the equation. -1.428571429 + 1.428571429 + t = -1.010152545 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + t = -1.010152545 + 1.428571429 t = -1.010152545 + 1.428571429 Combine like terms: -1.010152545 + 1.428571429 = 0.418418884 t = 0.418418884 Simplifying t = 0.418418884Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.438723974, 0.418418884}
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