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Simplifying 0 = (-4.9) * t2 + 21t + 60 Reorder the terms: 0 = 60 + 21t + -4.9t2 Solving 0 = 60 + 21t + -4.9t2 Solving for variable 't'. Combine like terms: 0 + -60 = -60 -60 + -21t + 4.9t2 = 60 + 21t + -4.9t2 + -60 + -21t + 4.9t2 Reorder the terms: -60 + -21t + 4.9t2 = 60 + -60 + 21t + -21t + -4.9t2 + 4.9t2 Combine like terms: 60 + -60 = 0 -60 + -21t + 4.9t2 = 0 + 21t + -21t + -4.9t2 + 4.9t2 -60 + -21t + 4.9t2 = 21t + -21t + -4.9t2 + 4.9t2 Combine like terms: 21t + -21t = 0 -60 + -21t + 4.9t2 = 0 + -4.9t2 + 4.9t2 -60 + -21t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -60 + -21t + 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'. -12.24489796 + -4.285714286t + t2 = 0 Move the constant term to the right: Add '12.24489796' to each side of the equation. -12.24489796 + -4.285714286t + 12.24489796 + t2 = 0 + 12.24489796 Reorder the terms: -12.24489796 + 12.24489796 + -4.285714286t + t2 = 0 + 12.24489796 Combine like terms: -12.24489796 + 12.24489796 = 0.00000000 0.00000000 + -4.285714286t + t2 = 0 + 12.24489796 -4.285714286t + t2 = 0 + 12.24489796 Combine like terms: 0 + 12.24489796 = 12.24489796 -4.285714286t + t2 = 12.24489796 The t term is -4.285714286t. Take half its coefficient (-2.142857143). Square it (4.591836735) and add it to both sides. Add '4.591836735' to each side of the equation. -4.285714286t + 4.591836735 + t2 = 12.24489796 + 4.591836735 Reorder the terms: 4.591836735 + -4.285714286t + t2 = 12.24489796 + 4.591836735 Combine like terms: 12.24489796 + 4.591836735 = 16.836734695 4.591836735 + -4.285714286t + t2 = 16.836734695 Factor a perfect square on the left side: (t + -2.142857143)(t + -2.142857143) = 16.836734695 Calculate the square root of the right side: 4.103259033 Break this problem into two subproblems by setting (t + -2.142857143) equal to 4.103259033 and -4.103259033.Subproblem 1
t + -2.142857143 = 4.103259033 Simplifying t + -2.142857143 = 4.103259033 Reorder the terms: -2.142857143 + t = 4.103259033 Solving -2.142857143 + t = 4.103259033 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.142857143' to each side of the equation. -2.142857143 + 2.142857143 + t = 4.103259033 + 2.142857143 Combine like terms: -2.142857143 + 2.142857143 = 0.000000000 0.000000000 + t = 4.103259033 + 2.142857143 t = 4.103259033 + 2.142857143 Combine like terms: 4.103259033 + 2.142857143 = 6.246116176 t = 6.246116176 Simplifying t = 6.246116176Subproblem 2
t + -2.142857143 = -4.103259033 Simplifying t + -2.142857143 = -4.103259033 Reorder the terms: -2.142857143 + t = -4.103259033 Solving -2.142857143 + t = -4.103259033 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.142857143' to each side of the equation. -2.142857143 + 2.142857143 + t = -4.103259033 + 2.142857143 Combine like terms: -2.142857143 + 2.142857143 = 0.000000000 0.000000000 + t = -4.103259033 + 2.142857143 t = -4.103259033 + 2.142857143 Combine like terms: -4.103259033 + 2.142857143 = -1.96040189 t = -1.96040189 Simplifying t = -1.96040189Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.246116176, -1.96040189}
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