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Simplifying 0 = 4.9t2 + -14t + 10 Reorder the terms: 0 = 10 + -14t + 4.9t2 Solving 0 = 10 + -14t + 4.9t2 Solving for variable 't'. Combine like terms: 0 + -10 = -10 -10 + 14t + -4.9t2 = 10 + -14t + 4.9t2 + -10 + 14t + -4.9t2 Reorder the terms: -10 + 14t + -4.9t2 = 10 + -10 + -14t + 14t + 4.9t2 + -4.9t2 Combine like terms: 10 + -10 = 0 -10 + 14t + -4.9t2 = 0 + -14t + 14t + 4.9t2 + -4.9t2 -10 + 14t + -4.9t2 = -14t + 14t + 4.9t2 + -4.9t2 Combine like terms: -14t + 14t = 0 -10 + 14t + -4.9t2 = 0 + 4.9t2 + -4.9t2 -10 + 14t + -4.9t2 = 4.9t2 + -4.9t2 Combine like terms: 4.9t2 + -4.9t2 = 0.0 -10 + 14t + -4.9t2 = 0.0 Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. 2.040816327 + -2.857142857t + t2 = 0 Move the constant term to the right: Add '-2.040816327' to each side of the equation. 2.040816327 + -2.857142857t + -2.040816327 + t2 = 0 + -2.040816327 Reorder the terms: 2.040816327 + -2.040816327 + -2.857142857t + t2 = 0 + -2.040816327 Combine like terms: 2.040816327 + -2.040816327 = 0.000000000 0.000000000 + -2.857142857t + t2 = 0 + -2.040816327 -2.857142857t + t2 = 0 + -2.040816327 Combine like terms: 0 + -2.040816327 = -2.040816327 -2.857142857t + t2 = -2.040816327 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 = -2.040816327 + 2.040816328 Reorder the terms: 2.040816328 + -2.857142857t + t2 = -2.040816327 + 2.040816328 Combine like terms: -2.040816327 + 2.040816328 = 0.000000001 2.040816328 + -2.857142857t + t2 = 0.000000001 Factor a perfect square on the left side: (t + -1.428571429)(t + -1.428571429) = 0.000000001 Calculate the square root of the right side: 0.000031623 Break this problem into two subproblems by setting (t + -1.428571429) equal to 0.000031623 and -0.000031623.Subproblem 1
t + -1.428571429 = 0.000031623 Simplifying t + -1.428571429 = 0.000031623 Reorder the terms: -1.428571429 + t = 0.000031623 Solving -1.428571429 + t = 0.000031623 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 = 0.000031623 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + t = 0.000031623 + 1.428571429 t = 0.000031623 + 1.428571429 Combine like terms: 0.000031623 + 1.428571429 = 1.428603052 t = 1.428603052 Simplifying t = 1.428603052Subproblem 2
t + -1.428571429 = -0.000031623 Simplifying t + -1.428571429 = -0.000031623 Reorder the terms: -1.428571429 + t = -0.000031623 Solving -1.428571429 + t = -0.000031623 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 = -0.000031623 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + t = -0.000031623 + 1.428571429 t = -0.000031623 + 1.428571429 Combine like terms: -0.000031623 + 1.428571429 = 1.428539806 t = 1.428539806 Simplifying t = 1.428539806Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.428603052, 1.428539806}
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