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Simplifying 3 + 22.5t + -4.9t2 = 0 Solving 3 + 22.5t + -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'. -0.612244898 + -4.591836735t + t2 = 0 Move the constant term to the right: Add '0.612244898' to each side of the equation. -0.612244898 + -4.591836735t + 0.612244898 + t2 = 0 + 0.612244898 Reorder the terms: -0.612244898 + 0.612244898 + -4.591836735t + t2 = 0 + 0.612244898 Combine like terms: -0.612244898 + 0.612244898 = 0.000000000 0.000000000 + -4.591836735t + t2 = 0 + 0.612244898 -4.591836735t + t2 = 0 + 0.612244898 Combine like terms: 0 + 0.612244898 = 0.612244898 -4.591836735t + t2 = 0.612244898 The t term is -4.591836735t. Take half its coefficient (-2.295918368). Square it (5.271241153) and add it to both sides. Add '5.271241153' to each side of the equation. -4.591836735t + 5.271241153 + t2 = 0.612244898 + 5.271241153 Reorder the terms: 5.271241153 + -4.591836735t + t2 = 0.612244898 + 5.271241153 Combine like terms: 0.612244898 + 5.271241153 = 5.883486051 5.271241153 + -4.591836735t + t2 = 5.883486051 Factor a perfect square on the left side: (t + -2.295918368)(t + -2.295918368) = 5.883486051 Calculate the square root of the right side: 2.425589836 Break this problem into two subproblems by setting (t + -2.295918368) equal to 2.425589836 and -2.425589836.Subproblem 1
t + -2.295918368 = 2.425589836 Simplifying t + -2.295918368 = 2.425589836 Reorder the terms: -2.295918368 + t = 2.425589836 Solving -2.295918368 + t = 2.425589836 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.295918368' to each side of the equation. -2.295918368 + 2.295918368 + t = 2.425589836 + 2.295918368 Combine like terms: -2.295918368 + 2.295918368 = 0.000000000 0.000000000 + t = 2.425589836 + 2.295918368 t = 2.425589836 + 2.295918368 Combine like terms: 2.425589836 + 2.295918368 = 4.721508204 t = 4.721508204 Simplifying t = 4.721508204Subproblem 2
t + -2.295918368 = -2.425589836 Simplifying t + -2.295918368 = -2.425589836 Reorder the terms: -2.295918368 + t = -2.425589836 Solving -2.295918368 + t = -2.425589836 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.295918368' to each side of the equation. -2.295918368 + 2.295918368 + t = -2.425589836 + 2.295918368 Combine like terms: -2.295918368 + 2.295918368 = 0.000000000 0.000000000 + t = -2.425589836 + 2.295918368 t = -2.425589836 + 2.295918368 Combine like terms: -2.425589836 + 2.295918368 = -0.129671468 t = -0.129671468 Simplifying t = -0.129671468Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.721508204, -0.129671468}
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