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Simplifying -4.9t2 + -42t + 170 = 0 Reorder the terms: 170 + -42t + -4.9t2 = 0 Solving 170 + -42t + -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'. -34.69387755 + 8.571428571t + t2 = 0 Move the constant term to the right: Add '34.69387755' to each side of the equation. -34.69387755 + 8.571428571t + 34.69387755 + t2 = 0 + 34.69387755 Reorder the terms: -34.69387755 + 34.69387755 + 8.571428571t + t2 = 0 + 34.69387755 Combine like terms: -34.69387755 + 34.69387755 = 0.00000000 0.00000000 + 8.571428571t + t2 = 0 + 34.69387755 8.571428571t + t2 = 0 + 34.69387755 Combine like terms: 0 + 34.69387755 = 34.69387755 8.571428571t + t2 = 34.69387755 The t term is 8.571428571t. Take half its coefficient (4.285714286). Square it (18.36734694) and add it to both sides. Add '18.36734694' to each side of the equation. 8.571428571t + 18.36734694 + t2 = 34.69387755 + 18.36734694 Reorder the terms: 18.36734694 + 8.571428571t + t2 = 34.69387755 + 18.36734694 Combine like terms: 34.69387755 + 18.36734694 = 53.06122449 18.36734694 + 8.571428571t + t2 = 53.06122449 Factor a perfect square on the left side: (t + 4.285714286)(t + 4.285714286) = 53.06122449 Calculate the square root of the right side: 7.284313591 Break this problem into two subproblems by setting (t + 4.285714286) equal to 7.284313591 and -7.284313591.Subproblem 1
t + 4.285714286 = 7.284313591 Simplifying t + 4.285714286 = 7.284313591 Reorder the terms: 4.285714286 + t = 7.284313591 Solving 4.285714286 + t = 7.284313591 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-4.285714286' to each side of the equation. 4.285714286 + -4.285714286 + t = 7.284313591 + -4.285714286 Combine like terms: 4.285714286 + -4.285714286 = 0.000000000 0.000000000 + t = 7.284313591 + -4.285714286 t = 7.284313591 + -4.285714286 Combine like terms: 7.284313591 + -4.285714286 = 2.998599305 t = 2.998599305 Simplifying t = 2.998599305Subproblem 2
t + 4.285714286 = -7.284313591 Simplifying t + 4.285714286 = -7.284313591 Reorder the terms: 4.285714286 + t = -7.284313591 Solving 4.285714286 + t = -7.284313591 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-4.285714286' to each side of the equation. 4.285714286 + -4.285714286 + t = -7.284313591 + -4.285714286 Combine like terms: 4.285714286 + -4.285714286 = 0.000000000 0.000000000 + t = -7.284313591 + -4.285714286 t = -7.284313591 + -4.285714286 Combine like terms: -7.284313591 + -4.285714286 = -11.570027877 t = -11.570027877 Simplifying t = -11.570027877Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.998599305, -11.570027877}
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