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Simplifying 750 = 4.9t2 + 7t Reorder the terms: 750 = 7t + 4.9t2 Solving 750 = 7t + 4.9t2 Solving for variable 't'. Reorder the terms: 750 + -7t + -4.9t2 = 7t + -7t + 4.9t2 + -4.9t2 Combine like terms: 7t + -7t = 0 750 + -7t + -4.9t2 = 0 + 4.9t2 + -4.9t2 750 + -7t + -4.9t2 = 4.9t2 + -4.9t2 Combine like terms: 4.9t2 + -4.9t2 = 0.0 750 + -7t + -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'. -153.0612245 + 1.428571429t + t2 = 0 Move the constant term to the right: Add '153.0612245' to each side of the equation. -153.0612245 + 1.428571429t + 153.0612245 + t2 = 0 + 153.0612245 Reorder the terms: -153.0612245 + 153.0612245 + 1.428571429t + t2 = 0 + 153.0612245 Combine like terms: -153.0612245 + 153.0612245 = 0.0000000 0.0000000 + 1.428571429t + t2 = 0 + 153.0612245 1.428571429t + t2 = 0 + 153.0612245 Combine like terms: 0 + 153.0612245 = 153.0612245 1.428571429t + t2 = 153.0612245 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 = 153.0612245 + 0.5102040819 Reorder the terms: 0.5102040819 + 1.428571429t + t2 = 153.0612245 + 0.5102040819 Combine like terms: 153.0612245 + 0.5102040819 = 153.5714285819 0.5102040819 + 1.428571429t + t2 = 153.5714285819 Factor a perfect square on the left side: (t + 0.7142857145)(t + 0.7142857145) = 153.5714285819 Calculate the square root of the right side: 12.392393981 Break this problem into two subproblems by setting (t + 0.7142857145) equal to 12.392393981 and -12.392393981.Subproblem 1
t + 0.7142857145 = 12.392393981 Simplifying t + 0.7142857145 = 12.392393981 Reorder the terms: 0.7142857145 + t = 12.392393981 Solving 0.7142857145 + t = 12.392393981 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 = 12.392393981 + -0.7142857145 Combine like terms: 0.7142857145 + -0.7142857145 = 0.0000000000 0.0000000000 + t = 12.392393981 + -0.7142857145 t = 12.392393981 + -0.7142857145 Combine like terms: 12.392393981 + -0.7142857145 = 11.6781082665 t = 11.6781082665 Simplifying t = 11.6781082665Subproblem 2
t + 0.7142857145 = -12.392393981 Simplifying t + 0.7142857145 = -12.392393981 Reorder the terms: 0.7142857145 + t = -12.392393981 Solving 0.7142857145 + t = -12.392393981 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 = -12.392393981 + -0.7142857145 Combine like terms: 0.7142857145 + -0.7142857145 = 0.0000000000 0.0000000000 + t = -12.392393981 + -0.7142857145 t = -12.392393981 + -0.7142857145 Combine like terms: -12.392393981 + -0.7142857145 = -13.1066796955 t = -13.1066796955 Simplifying t = -13.1066796955Solution
The solution to the problem is based on the solutions from the subproblems. t = {11.6781082665, -13.1066796955}
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