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Simplifying 0 = 4.9t2 + 13.79t + -9.70 Reorder the terms: 0 = -9.70 + 13.79t + 4.9t2 Solving 0 = -9.70 + 13.79t + 4.9t2 Solving for variable 't'. Combine like terms: 0 + 9.70 = 9.7 9.7 + -13.79t + -4.9t2 = -9.70 + 13.79t + 4.9t2 + 9.70 + -13.79t + -4.9t2 Reorder the terms: 9.7 + -13.79t + -4.9t2 = -9.70 + 9.70 + 13.79t + -13.79t + 4.9t2 + -4.9t2 Combine like terms: -9.70 + 9.70 = 0.00 9.7 + -13.79t + -4.9t2 = 0.00 + 13.79t + -13.79t + 4.9t2 + -4.9t2 9.7 + -13.79t + -4.9t2 = 13.79t + -13.79t + 4.9t2 + -4.9t2 Combine like terms: 13.79t + -13.79t = 0.00 9.7 + -13.79t + -4.9t2 = 0.00 + 4.9t2 + -4.9t2 9.7 + -13.79t + -4.9t2 = 4.9t2 + -4.9t2 Combine like terms: 4.9t2 + -4.9t2 = 0.0 9.7 + -13.79t + -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'. -1.979591837 + 2.814285714t + t2 = 0 Move the constant term to the right: Add '1.979591837' to each side of the equation. -1.979591837 + 2.814285714t + 1.979591837 + t2 = 0 + 1.979591837 Reorder the terms: -1.979591837 + 1.979591837 + 2.814285714t + t2 = 0 + 1.979591837 Combine like terms: -1.979591837 + 1.979591837 = 0.000000000 0.000000000 + 2.814285714t + t2 = 0 + 1.979591837 2.814285714t + t2 = 0 + 1.979591837 Combine like terms: 0 + 1.979591837 = 1.979591837 2.814285714t + t2 = 1.979591837 The t term is 2.814285714t. Take half its coefficient (1.407142857). Square it (1.980051020) and add it to both sides. Add '1.980051020' to each side of the equation. 2.814285714t + 1.980051020 + t2 = 1.979591837 + 1.980051020 Reorder the terms: 1.980051020 + 2.814285714t + t2 = 1.979591837 + 1.980051020 Combine like terms: 1.979591837 + 1.980051020 = 3.959642857 1.980051020 + 2.814285714t + t2 = 3.959642857 Factor a perfect square on the left side: (t + 1.407142857)(t + 1.407142857) = 3.959642857 Calculate the square root of the right side: 1.989885137 Break this problem into two subproblems by setting (t + 1.407142857) equal to 1.989885137 and -1.989885137.Subproblem 1
t + 1.407142857 = 1.989885137 Simplifying t + 1.407142857 = 1.989885137 Reorder the terms: 1.407142857 + t = 1.989885137 Solving 1.407142857 + t = 1.989885137 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.407142857' to each side of the equation. 1.407142857 + -1.407142857 + t = 1.989885137 + -1.407142857 Combine like terms: 1.407142857 + -1.407142857 = 0.000000000 0.000000000 + t = 1.989885137 + -1.407142857 t = 1.989885137 + -1.407142857 Combine like terms: 1.989885137 + -1.407142857 = 0.58274228 t = 0.58274228 Simplifying t = 0.58274228Subproblem 2
t + 1.407142857 = -1.989885137 Simplifying t + 1.407142857 = -1.989885137 Reorder the terms: 1.407142857 + t = -1.989885137 Solving 1.407142857 + t = -1.989885137 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.407142857' to each side of the equation. 1.407142857 + -1.407142857 + t = -1.989885137 + -1.407142857 Combine like terms: 1.407142857 + -1.407142857 = 0.000000000 0.000000000 + t = -1.989885137 + -1.407142857 t = -1.989885137 + -1.407142857 Combine like terms: -1.989885137 + -1.407142857 = -3.397027994 t = -3.397027994 Simplifying t = -3.397027994Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.58274228, -3.397027994}
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