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Simplifying -4.9t2 + 43.4t + 6.3 = 0 Reorder the terms: 6.3 + 43.4t + -4.9t2 = 0 Solving 6.3 + 43.4t + -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'. -1.285714286 + -8.857142857t + t2 = 0 Move the constant term to the right: Add '1.285714286' to each side of the equation. -1.285714286 + -8.857142857t + 1.285714286 + t2 = 0 + 1.285714286 Reorder the terms: -1.285714286 + 1.285714286 + -8.857142857t + t2 = 0 + 1.285714286 Combine like terms: -1.285714286 + 1.285714286 = 0.000000000 0.000000000 + -8.857142857t + t2 = 0 + 1.285714286 -8.857142857t + t2 = 0 + 1.285714286 Combine like terms: 0 + 1.285714286 = 1.285714286 -8.857142857t + t2 = 1.285714286 The t term is -8.857142857t. Take half its coefficient (-4.428571429). Square it (19.61224490) and add it to both sides. Add '19.61224490' to each side of the equation. -8.857142857t + 19.61224490 + t2 = 1.285714286 + 19.61224490 Reorder the terms: 19.61224490 + -8.857142857t + t2 = 1.285714286 + 19.61224490 Combine like terms: 1.285714286 + 19.61224490 = 20.897959186 19.61224490 + -8.857142857t + t2 = 20.897959186 Factor a perfect square on the left side: (t + -4.428571429)(t + -4.428571429) = 20.897959186 Calculate the square root of the right side: 4.571428572 Break this problem into two subproblems by setting (t + -4.428571429) equal to 4.571428572 and -4.571428572.Subproblem 1
t + -4.428571429 = 4.571428572 Simplifying t + -4.428571429 = 4.571428572 Reorder the terms: -4.428571429 + t = 4.571428572 Solving -4.428571429 + t = 4.571428572 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.428571429' to each side of the equation. -4.428571429 + 4.428571429 + t = 4.571428572 + 4.428571429 Combine like terms: -4.428571429 + 4.428571429 = 0.000000000 0.000000000 + t = 4.571428572 + 4.428571429 t = 4.571428572 + 4.428571429 Combine like terms: 4.571428572 + 4.428571429 = 9.000000001 t = 9.000000001 Simplifying t = 9.000000001Subproblem 2
t + -4.428571429 = -4.571428572 Simplifying t + -4.428571429 = -4.571428572 Reorder the terms: -4.428571429 + t = -4.571428572 Solving -4.428571429 + t = -4.571428572 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.428571429' to each side of the equation. -4.428571429 + 4.428571429 + t = -4.571428572 + 4.428571429 Combine like terms: -4.428571429 + 4.428571429 = 0.000000000 0.000000000 + t = -4.571428572 + 4.428571429 t = -4.571428572 + 4.428571429 Combine like terms: -4.571428572 + 4.428571429 = -0.142857143 t = -0.142857143 Simplifying t = -0.142857143Solution
The solution to the problem is based on the solutions from the subproblems. t = {9.000000001, -0.142857143}
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