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Simplifying 4.9t2 + 7t + -20 = 0 Reorder the terms: -20 + 7t + 4.9t2 = 0 Solving -20 + 7t + 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'. -4.081632653 + 1.428571429t + t2 = 0 Move the constant term to the right: Add '4.081632653' to each side of the equation. -4.081632653 + 1.428571429t + 4.081632653 + t2 = 0 + 4.081632653 Reorder the terms: -4.081632653 + 4.081632653 + 1.428571429t + t2 = 0 + 4.081632653 Combine like terms: -4.081632653 + 4.081632653 = 0.000000000 0.000000000 + 1.428571429t + t2 = 0 + 4.081632653 1.428571429t + t2 = 0 + 4.081632653 Combine like terms: 0 + 4.081632653 = 4.081632653 1.428571429t + t2 = 4.081632653 The t term is 1.428571429t. Take half its coefficient (0.7142857145). Square it (0.5102040819) and add it to both sides. Add '0.5102040819' to each side of the equation. 1.428571429t + 0.5102040819 + t2 = 4.081632653 + 0.5102040819 Reorder the terms: 0.5102040819 + 1.428571429t + t2 = 4.081632653 + 0.5102040819 Combine like terms: 4.081632653 + 0.5102040819 = 4.5918367349 0.5102040819 + 1.428571429t + t2 = 4.5918367349 Factor a perfect square on the left side: (t + 0.7142857145)(t + 0.7142857145) = 4.5918367349 Calculate the square root of the right side: 2.142857143 Break this problem into two subproblems by setting (t + 0.7142857145) equal to 2.142857143 and -2.142857143.Subproblem 1
t + 0.7142857145 = 2.142857143 Simplifying t + 0.7142857145 = 2.142857143 Reorder the terms: 0.7142857145 + t = 2.142857143 Solving 0.7142857145 + t = 2.142857143 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.7142857145' to each side of the equation. 0.7142857145 + -0.7142857145 + t = 2.142857143 + -0.7142857145 Combine like terms: 0.7142857145 + -0.7142857145 = 0.0000000000 0.0000000000 + t = 2.142857143 + -0.7142857145 t = 2.142857143 + -0.7142857145 Combine like terms: 2.142857143 + -0.7142857145 = 1.4285714285 t = 1.4285714285 Simplifying t = 1.4285714285Subproblem 2
t + 0.7142857145 = -2.142857143 Simplifying t + 0.7142857145 = -2.142857143 Reorder the terms: 0.7142857145 + t = -2.142857143 Solving 0.7142857145 + t = -2.142857143 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.7142857145' to each side of the equation. 0.7142857145 + -0.7142857145 + t = -2.142857143 + -0.7142857145 Combine like terms: 0.7142857145 + -0.7142857145 = 0.0000000000 0.0000000000 + t = -2.142857143 + -0.7142857145 t = -2.142857143 + -0.7142857145 Combine like terms: -2.142857143 + -0.7142857145 = -2.8571428575 t = -2.8571428575 Simplifying t = -2.8571428575Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.4285714285, -2.8571428575}
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