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Simplifying 4.9t2 + -7t + -15 = 0 Reorder the terms: -15 + -7t + 4.9t2 = 0 Solving -15 + -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'. -3.06122449 + -1.428571429t + t2 = 0 Move the constant term to the right: Add '3.06122449' to each side of the equation. -3.06122449 + -1.428571429t + 3.06122449 + t2 = 0 + 3.06122449 Reorder the terms: -3.06122449 + 3.06122449 + -1.428571429t + t2 = 0 + 3.06122449 Combine like terms: -3.06122449 + 3.06122449 = 0.00000000 0.00000000 + -1.428571429t + t2 = 0 + 3.06122449 -1.428571429t + t2 = 0 + 3.06122449 Combine like terms: 0 + 3.06122449 = 3.06122449 -1.428571429t + t2 = 3.06122449 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 = 3.06122449 + 0.5102040819 Reorder the terms: 0.5102040819 + -1.428571429t + t2 = 3.06122449 + 0.5102040819 Combine like terms: 3.06122449 + 0.5102040819 = 3.5714285719 0.5102040819 + -1.428571429t + t2 = 3.5714285719 Factor a perfect square on the left side: (t + -0.7142857145)(t + -0.7142857145) = 3.5714285719 Calculate the square root of the right side: 1.889822365 Break this problem into two subproblems by setting (t + -0.7142857145) equal to 1.889822365 and -1.889822365.Subproblem 1
t + -0.7142857145 = 1.889822365 Simplifying t + -0.7142857145 = 1.889822365 Reorder the terms: -0.7142857145 + t = 1.889822365 Solving -0.7142857145 + t = 1.889822365 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 = 1.889822365 + 0.7142857145 Combine like terms: -0.7142857145 + 0.7142857145 = 0.0000000000 0.0000000000 + t = 1.889822365 + 0.7142857145 t = 1.889822365 + 0.7142857145 Combine like terms: 1.889822365 + 0.7142857145 = 2.6041080795 t = 2.6041080795 Simplifying t = 2.6041080795Subproblem 2
t + -0.7142857145 = -1.889822365 Simplifying t + -0.7142857145 = -1.889822365 Reorder the terms: -0.7142857145 + t = -1.889822365 Solving -0.7142857145 + t = -1.889822365 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 = -1.889822365 + 0.7142857145 Combine like terms: -0.7142857145 + 0.7142857145 = 0.0000000000 0.0000000000 + t = -1.889822365 + 0.7142857145 t = -1.889822365 + 0.7142857145 Combine like terms: -1.889822365 + 0.7142857145 = -1.1755366505 t = -1.1755366505 Simplifying t = -1.1755366505Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.6041080795, -1.1755366505}
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