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Simplifying -4.9t2 + 21t + 120 = 0 Reorder the terms: 120 + 21t + -4.9t2 = 0 Solving 120 + 21t + -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'. -24.48979592 + -4.285714286t + t2 = 0 Move the constant term to the right: Add '24.48979592' to each side of the equation. -24.48979592 + -4.285714286t + 24.48979592 + t2 = 0 + 24.48979592 Reorder the terms: -24.48979592 + 24.48979592 + -4.285714286t + t2 = 0 + 24.48979592 Combine like terms: -24.48979592 + 24.48979592 = 0.00000000 0.00000000 + -4.285714286t + t2 = 0 + 24.48979592 -4.285714286t + t2 = 0 + 24.48979592 Combine like terms: 0 + 24.48979592 = 24.48979592 -4.285714286t + t2 = 24.48979592 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 = 24.48979592 + 4.591836735 Reorder the terms: 4.591836735 + -4.285714286t + t2 = 24.48979592 + 4.591836735 Combine like terms: 24.48979592 + 4.591836735 = 29.081632655 4.591836735 + -4.285714286t + t2 = 29.081632655 Factor a perfect square on the left side: (t + -2.142857143)(t + -2.142857143) = 29.081632655 Calculate the square root of the right side: 5.392738883 Break this problem into two subproblems by setting (t + -2.142857143) equal to 5.392738883 and -5.392738883.Subproblem 1
t + -2.142857143 = 5.392738883 Simplifying t + -2.142857143 = 5.392738883 Reorder the terms: -2.142857143 + t = 5.392738883 Solving -2.142857143 + t = 5.392738883 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 = 5.392738883 + 2.142857143 Combine like terms: -2.142857143 + 2.142857143 = 0.000000000 0.000000000 + t = 5.392738883 + 2.142857143 t = 5.392738883 + 2.142857143 Combine like terms: 5.392738883 + 2.142857143 = 7.535596026 t = 7.535596026 Simplifying t = 7.535596026Subproblem 2
t + -2.142857143 = -5.392738883 Simplifying t + -2.142857143 = -5.392738883 Reorder the terms: -2.142857143 + t = -5.392738883 Solving -2.142857143 + t = -5.392738883 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 = -5.392738883 + 2.142857143 Combine like terms: -2.142857143 + 2.142857143 = 0.000000000 0.000000000 + t = -5.392738883 + 2.142857143 t = -5.392738883 + 2.142857143 Combine like terms: -5.392738883 + 2.142857143 = -3.24988174 t = -3.24988174 Simplifying t = -3.24988174Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.535596026, -3.24988174}
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