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Simplifying 0 = -4.9t2 + 13t + 3 Reorder the terms: 0 = 3 + 13t + -4.9t2 Solving 0 = 3 + 13t + -4.9t2 Solving for variable 't'. Combine like terms: 0 + -3 = -3 -3 + -13t + 4.9t2 = 3 + 13t + -4.9t2 + -3 + -13t + 4.9t2 Reorder the terms: -3 + -13t + 4.9t2 = 3 + -3 + 13t + -13t + -4.9t2 + 4.9t2 Combine like terms: 3 + -3 = 0 -3 + -13t + 4.9t2 = 0 + 13t + -13t + -4.9t2 + 4.9t2 -3 + -13t + 4.9t2 = 13t + -13t + -4.9t2 + 4.9t2 Combine like terms: 13t + -13t = 0 -3 + -13t + 4.9t2 = 0 + -4.9t2 + 4.9t2 -3 + -13t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -3 + -13t + 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'. -0.612244898 + -2.653061224t + t2 = 0 Move the constant term to the right: Add '0.612244898' to each side of the equation. -0.612244898 + -2.653061224t + 0.612244898 + t2 = 0 + 0.612244898 Reorder the terms: -0.612244898 + 0.612244898 + -2.653061224t + t2 = 0 + 0.612244898 Combine like terms: -0.612244898 + 0.612244898 = 0.000000000 0.000000000 + -2.653061224t + t2 = 0 + 0.612244898 -2.653061224t + t2 = 0 + 0.612244898 Combine like terms: 0 + 0.612244898 = 0.612244898 -2.653061224t + t2 = 0.612244898 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 = 0.612244898 + 1.759683465 Reorder the terms: 1.759683465 + -2.653061224t + t2 = 0.612244898 + 1.759683465 Combine like terms: 0.612244898 + 1.759683465 = 2.371928363 1.759683465 + -2.653061224t + t2 = 2.371928363 Factor a perfect square on the left side: (t + -1.326530612)(t + -1.326530612) = 2.371928363 Calculate the square root of the right side: 1.540106608 Break this problem into two subproblems by setting (t + -1.326530612) equal to 1.540106608 and -1.540106608.Subproblem 1
t + -1.326530612 = 1.540106608 Simplifying t + -1.326530612 = 1.540106608 Reorder the terms: -1.326530612 + t = 1.540106608 Solving -1.326530612 + t = 1.540106608 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 = 1.540106608 + 1.326530612 Combine like terms: -1.326530612 + 1.326530612 = 0.000000000 0.000000000 + t = 1.540106608 + 1.326530612 t = 1.540106608 + 1.326530612 Combine like terms: 1.540106608 + 1.326530612 = 2.86663722 t = 2.86663722 Simplifying t = 2.86663722Subproblem 2
t + -1.326530612 = -1.540106608 Simplifying t + -1.326530612 = -1.540106608 Reorder the terms: -1.326530612 + t = -1.540106608 Solving -1.326530612 + t = -1.540106608 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 = -1.540106608 + 1.326530612 Combine like terms: -1.326530612 + 1.326530612 = 0.000000000 0.000000000 + t = -1.540106608 + 1.326530612 t = -1.540106608 + 1.326530612 Combine like terms: -1.540106608 + 1.326530612 = -0.213575996 t = -0.213575996 Simplifying t = -0.213575996Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.86663722, -0.213575996}
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