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Simplifying -4.9t2 + 6t + 0.5 = 0 Reorder the terms: 0.5 + 6t + -4.9t2 = 0 Solving 0.5 + 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'. -0.1020408163 + -1.224489796t + t2 = 0 Move the constant term to the right: Add '0.1020408163' to each side of the equation. -0.1020408163 + -1.224489796t + 0.1020408163 + t2 = 0 + 0.1020408163 Reorder the terms: -0.1020408163 + 0.1020408163 + -1.224489796t + t2 = 0 + 0.1020408163 Combine like terms: -0.1020408163 + 0.1020408163 = 0.0000000000 0.0000000000 + -1.224489796t + t2 = 0 + 0.1020408163 -1.224489796t + t2 = 0 + 0.1020408163 Combine like terms: 0 + 0.1020408163 = 0.1020408163 -1.224489796t + t2 = 0.1020408163 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 = 0.1020408163 + 0.3748438151 Reorder the terms: 0.3748438151 + -1.224489796t + t2 = 0.1020408163 + 0.3748438151 Combine like terms: 0.1020408163 + 0.3748438151 = 0.4768846314 0.3748438151 + -1.224489796t + t2 = 0.4768846314 Factor a perfect square on the left side: (t + -0.612244898)(t + -0.612244898) = 0.4768846314 Calculate the square root of the right side: 0.690568339 Break this problem into two subproblems by setting (t + -0.612244898) equal to 0.690568339 and -0.690568339.Subproblem 1
t + -0.612244898 = 0.690568339 Simplifying t + -0.612244898 = 0.690568339 Reorder the terms: -0.612244898 + t = 0.690568339 Solving -0.612244898 + t = 0.690568339 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 = 0.690568339 + 0.612244898 Combine like terms: -0.612244898 + 0.612244898 = 0.000000000 0.000000000 + t = 0.690568339 + 0.612244898 t = 0.690568339 + 0.612244898 Combine like terms: 0.690568339 + 0.612244898 = 1.302813237 t = 1.302813237 Simplifying t = 1.302813237Subproblem 2
t + -0.612244898 = -0.690568339 Simplifying t + -0.612244898 = -0.690568339 Reorder the terms: -0.612244898 + t = -0.690568339 Solving -0.612244898 + t = -0.690568339 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 = -0.690568339 + 0.612244898 Combine like terms: -0.612244898 + 0.612244898 = 0.000000000 0.000000000 + t = -0.690568339 + 0.612244898 t = -0.690568339 + 0.612244898 Combine like terms: -0.690568339 + 0.612244898 = -0.078323441 t = -0.078323441 Simplifying t = -0.078323441Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.302813237, -0.078323441}
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