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Simplifying 7t2 + -20t = 13 Reorder the terms: -20t + 7t2 = 13 Solving -20t + 7t2 = 13 Solving for variable 't'. Reorder the terms: -13 + -20t + 7t2 = 13 + -13 Combine like terms: 13 + -13 = 0 -13 + -20t + 7t2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1.857142857 + -2.857142857t + t2 = 0 Move the constant term to the right: Add '1.857142857' to each side of the equation. -1.857142857 + -2.857142857t + 1.857142857 + t2 = 0 + 1.857142857 Reorder the terms: -1.857142857 + 1.857142857 + -2.857142857t + t2 = 0 + 1.857142857 Combine like terms: -1.857142857 + 1.857142857 = 0.000000000 0.000000000 + -2.857142857t + t2 = 0 + 1.857142857 -2.857142857t + t2 = 0 + 1.857142857 Combine like terms: 0 + 1.857142857 = 1.857142857 -2.857142857t + t2 = 1.857142857 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 = 1.857142857 + 2.040816328 Reorder the terms: 2.040816328 + -2.857142857t + t2 = 1.857142857 + 2.040816328 Combine like terms: 1.857142857 + 2.040816328 = 3.897959185 2.040816328 + -2.857142857t + t2 = 3.897959185 Factor a perfect square on the left side: (t + -1.428571429)(t + -1.428571429) = 3.897959185 Calculate the square root of the right side: 1.974324995 Break this problem into two subproblems by setting (t + -1.428571429) equal to 1.974324995 and -1.974324995.Subproblem 1
t + -1.428571429 = 1.974324995 Simplifying t + -1.428571429 = 1.974324995 Reorder the terms: -1.428571429 + t = 1.974324995 Solving -1.428571429 + t = 1.974324995 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 = 1.974324995 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + t = 1.974324995 + 1.428571429 t = 1.974324995 + 1.428571429 Combine like terms: 1.974324995 + 1.428571429 = 3.402896424 t = 3.402896424 Simplifying t = 3.402896424Subproblem 2
t + -1.428571429 = -1.974324995 Simplifying t + -1.428571429 = -1.974324995 Reorder the terms: -1.428571429 + t = -1.974324995 Solving -1.428571429 + t = -1.974324995 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 = -1.974324995 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + t = -1.974324995 + 1.428571429 t = -1.974324995 + 1.428571429 Combine like terms: -1.974324995 + 1.428571429 = -0.545753566 t = -0.545753566 Simplifying t = -0.545753566Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.402896424, -0.545753566}
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