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Simplifying 4.9t2 + 14t + -10 = 0 Reorder the terms: -10 + 14t + 4.9t2 = 0 Solving -10 + 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'. -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 = 4.081632655 2.040816328 + 2.857142857t + t2 = 4.081632655 Factor a perfect square on the left side: (t + 1.428571429)(t + 1.428571429) = 4.081632655 Calculate the square root of the right side: 2.02030509 Break this problem into two subproblems by setting (t + 1.428571429) equal to 2.02030509 and -2.02030509.Subproblem 1
t + 1.428571429 = 2.02030509 Simplifying t + 1.428571429 = 2.02030509 Reorder the terms: 1.428571429 + t = 2.02030509 Solving 1.428571429 + t = 2.02030509 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 = 2.02030509 + -1.428571429 Combine like terms: 1.428571429 + -1.428571429 = 0.000000000 0.000000000 + t = 2.02030509 + -1.428571429 t = 2.02030509 + -1.428571429 Combine like terms: 2.02030509 + -1.428571429 = 0.591733661 t = 0.591733661 Simplifying t = 0.591733661Subproblem 2
t + 1.428571429 = -2.02030509 Simplifying t + 1.428571429 = -2.02030509 Reorder the terms: 1.428571429 + t = -2.02030509 Solving 1.428571429 + t = -2.02030509 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 = -2.02030509 + -1.428571429 Combine like terms: 1.428571429 + -1.428571429 = 0.000000000 0.000000000 + t = -2.02030509 + -1.428571429 t = -2.02030509 + -1.428571429 Combine like terms: -2.02030509 + -1.428571429 = -3.448876519 t = -3.448876519 Simplifying t = -3.448876519Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.591733661, -3.448876519}
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