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Simplifying 4.9t2 + 6t + -100 = 0 Reorder the terms: -100 + 6t + 4.9t2 = 0 Solving -100 + 6t + 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'. -20.40816327 + 1.224489796t + t2 = 0 Move the constant term to the right: Add '20.40816327' to each side of the equation. -20.40816327 + 1.224489796t + 20.40816327 + t2 = 0 + 20.40816327 Reorder the terms: -20.40816327 + 20.40816327 + 1.224489796t + t2 = 0 + 20.40816327 Combine like terms: -20.40816327 + 20.40816327 = 0.00000000 0.00000000 + 1.224489796t + t2 = 0 + 20.40816327 1.224489796t + t2 = 0 + 20.40816327 Combine like terms: 0 + 20.40816327 = 20.40816327 1.224489796t + t2 = 20.40816327 The t term is 1.224489796t. Take half its coefficient (0.612244898). Square it (0.3748438151) and add it to both sides. Add '0.3748438151' to each side of the equation. 1.224489796t + 0.3748438151 + t2 = 20.40816327 + 0.3748438151 Reorder the terms: 0.3748438151 + 1.224489796t + t2 = 20.40816327 + 0.3748438151 Combine like terms: 20.40816327 + 0.3748438151 = 20.7830070851 0.3748438151 + 1.224489796t + t2 = 20.7830070851 Factor a perfect square on the left side: (t + 0.612244898)(t + 0.612244898) = 20.7830070851 Calculate the square root of the right side: 4.558838348 Break this problem into two subproblems by setting (t + 0.612244898) equal to 4.558838348 and -4.558838348.Subproblem 1
t + 0.612244898 = 4.558838348 Simplifying t + 0.612244898 = 4.558838348 Reorder the terms: 0.612244898 + t = 4.558838348 Solving 0.612244898 + t = 4.558838348 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.612244898' to each side of the equation. 0.612244898 + -0.612244898 + t = 4.558838348 + -0.612244898 Combine like terms: 0.612244898 + -0.612244898 = 0.000000000 0.000000000 + t = 4.558838348 + -0.612244898 t = 4.558838348 + -0.612244898 Combine like terms: 4.558838348 + -0.612244898 = 3.94659345 t = 3.94659345 Simplifying t = 3.94659345Subproblem 2
t + 0.612244898 = -4.558838348 Simplifying t + 0.612244898 = -4.558838348 Reorder the terms: 0.612244898 + t = -4.558838348 Solving 0.612244898 + t = -4.558838348 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.612244898' to each side of the equation. 0.612244898 + -0.612244898 + t = -4.558838348 + -0.612244898 Combine like terms: 0.612244898 + -0.612244898 = 0.000000000 0.000000000 + t = -4.558838348 + -0.612244898 t = -4.558838348 + -0.612244898 Combine like terms: -4.558838348 + -0.612244898 = -5.171083246 t = -5.171083246 Simplifying t = -5.171083246Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.94659345, -5.171083246}
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