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Simplifying -4.9t2 + 13t + 700 = 0 Reorder the terms: 700 + 13t + -4.9t2 = 0 Solving 700 + 13t + -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'. -142.8571429 + -2.653061224t + t2 = 0 Move the constant term to the right: Add '142.8571429' to each side of the equation. -142.8571429 + -2.653061224t + 142.8571429 + t2 = 0 + 142.8571429 Reorder the terms: -142.8571429 + 142.8571429 + -2.653061224t + t2 = 0 + 142.8571429 Combine like terms: -142.8571429 + 142.8571429 = 0.0000000 0.0000000 + -2.653061224t + t2 = 0 + 142.8571429 -2.653061224t + t2 = 0 + 142.8571429 Combine like terms: 0 + 142.8571429 = 142.8571429 -2.653061224t + t2 = 142.8571429 The t term is -2.653061224t. Take half its coefficient (-1.326530612). Square it (1.759683465) and add it to both sides. Add '1.759683465' to each side of the equation. -2.653061224t + 1.759683465 + t2 = 142.8571429 + 1.759683465 Reorder the terms: 1.759683465 + -2.653061224t + t2 = 142.8571429 + 1.759683465 Combine like terms: 142.8571429 + 1.759683465 = 144.616826365 1.759683465 + -2.653061224t + t2 = 144.616826365 Factor a perfect square on the left side: (t + -1.326530612)(t + -1.326530612) = 144.616826365 Calculate the square root of the right side: 12.025673635 Break this problem into two subproblems by setting (t + -1.326530612) equal to 12.025673635 and -12.025673635.Subproblem 1
t + -1.326530612 = 12.025673635 Simplifying t + -1.326530612 = 12.025673635 Reorder the terms: -1.326530612 + t = 12.025673635 Solving -1.326530612 + t = 12.025673635 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.326530612' to each side of the equation. -1.326530612 + 1.326530612 + t = 12.025673635 + 1.326530612 Combine like terms: -1.326530612 + 1.326530612 = 0.000000000 0.000000000 + t = 12.025673635 + 1.326530612 t = 12.025673635 + 1.326530612 Combine like terms: 12.025673635 + 1.326530612 = 13.352204247 t = 13.352204247 Simplifying t = 13.352204247Subproblem 2
t + -1.326530612 = -12.025673635 Simplifying t + -1.326530612 = -12.025673635 Reorder the terms: -1.326530612 + t = -12.025673635 Solving -1.326530612 + t = -12.025673635 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.326530612' to each side of the equation. -1.326530612 + 1.326530612 + t = -12.025673635 + 1.326530612 Combine like terms: -1.326530612 + 1.326530612 = 0.000000000 0.000000000 + t = -12.025673635 + 1.326530612 t = -12.025673635 + 1.326530612 Combine like terms: -12.025673635 + 1.326530612 = -10.699143023 t = -10.699143023 Simplifying t = -10.699143023Solution
The solution to the problem is based on the solutions from the subproblems. t = {13.352204247, -10.699143023}
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