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Simplifying -4.9t2 + 14.0t + 2.1 = 0 Reorder the terms: 2.1 + 14.0t + -4.9t2 = 0 Solving 2.1 + 14.0t + -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'. -0.4285714286 + -2.857142857t + t2 = 0 Move the constant term to the right: Add '0.4285714286' to each side of the equation. -0.4285714286 + -2.857142857t + 0.4285714286 + t2 = 0 + 0.4285714286 Reorder the terms: -0.4285714286 + 0.4285714286 + -2.857142857t + t2 = 0 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + -2.857142857t + t2 = 0 + 0.4285714286 -2.857142857t + t2 = 0 + 0.4285714286 Combine like terms: 0 + 0.4285714286 = 0.4285714286 -2.857142857t + t2 = 0.4285714286 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 = 0.4285714286 + 2.040816328 Reorder the terms: 2.040816328 + -2.857142857t + t2 = 0.4285714286 + 2.040816328 Combine like terms: 0.4285714286 + 2.040816328 = 2.4693877566 2.040816328 + -2.857142857t + t2 = 2.4693877566 Factor a perfect square on the left side: (t + -1.428571429)(t + -1.428571429) = 2.4693877566 Calculate the square root of the right side: 1.571428572 Break this problem into two subproblems by setting (t + -1.428571429) equal to 1.571428572 and -1.571428572.Subproblem 1
t + -1.428571429 = 1.571428572 Simplifying t + -1.428571429 = 1.571428572 Reorder the terms: -1.428571429 + t = 1.571428572 Solving -1.428571429 + t = 1.571428572 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 = 1.571428572 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + t = 1.571428572 + 1.428571429 t = 1.571428572 + 1.428571429 Combine like terms: 1.571428572 + 1.428571429 = 3.000000001 t = 3.000000001 Simplifying t = 3.000000001Subproblem 2
t + -1.428571429 = -1.571428572 Simplifying t + -1.428571429 = -1.571428572 Reorder the terms: -1.428571429 + t = -1.571428572 Solving -1.428571429 + t = -1.571428572 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 = -1.571428572 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + t = -1.571428572 + 1.428571429 t = -1.571428572 + 1.428571429 Combine like terms: -1.571428572 + 1.428571429 = -0.142857143 t = -0.142857143 Simplifying t = -0.142857143Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.000000001, -0.142857143}
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