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Simplifying -4.9t2 + 30.5t + 9.9 = 0 Reorder the terms: 9.9 + 30.5t + -4.9t2 = 0 Solving 9.9 + 30.5t + -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'. -2.020408163 + -6.224489796t + t2 = 0 Move the constant term to the right: Add '2.020408163' to each side of the equation. -2.020408163 + -6.224489796t + 2.020408163 + t2 = 0 + 2.020408163 Reorder the terms: -2.020408163 + 2.020408163 + -6.224489796t + t2 = 0 + 2.020408163 Combine like terms: -2.020408163 + 2.020408163 = 0.000000000 0.000000000 + -6.224489796t + t2 = 0 + 2.020408163 -6.224489796t + t2 = 0 + 2.020408163 Combine like terms: 0 + 2.020408163 = 2.020408163 -6.224489796t + t2 = 2.020408163 The t term is -6.224489796t. Take half its coefficient (-3.112244898). Square it (9.686068305) and add it to both sides. Add '9.686068305' to each side of the equation. -6.224489796t + 9.686068305 + t2 = 2.020408163 + 9.686068305 Reorder the terms: 9.686068305 + -6.224489796t + t2 = 2.020408163 + 9.686068305 Combine like terms: 2.020408163 + 9.686068305 = 11.706476468 9.686068305 + -6.224489796t + t2 = 11.706476468 Factor a perfect square on the left side: (t + -3.112244898)(t + -3.112244898) = 11.706476468 Calculate the square root of the right side: 3.421472851 Break this problem into two subproblems by setting (t + -3.112244898) equal to 3.421472851 and -3.421472851.Subproblem 1
t + -3.112244898 = 3.421472851 Simplifying t + -3.112244898 = 3.421472851 Reorder the terms: -3.112244898 + t = 3.421472851 Solving -3.112244898 + t = 3.421472851 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.112244898' to each side of the equation. -3.112244898 + 3.112244898 + t = 3.421472851 + 3.112244898 Combine like terms: -3.112244898 + 3.112244898 = 0.000000000 0.000000000 + t = 3.421472851 + 3.112244898 t = 3.421472851 + 3.112244898 Combine like terms: 3.421472851 + 3.112244898 = 6.533717749 t = 6.533717749 Simplifying t = 6.533717749Subproblem 2
t + -3.112244898 = -3.421472851 Simplifying t + -3.112244898 = -3.421472851 Reorder the terms: -3.112244898 + t = -3.421472851 Solving -3.112244898 + t = -3.421472851 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.112244898' to each side of the equation. -3.112244898 + 3.112244898 + t = -3.421472851 + 3.112244898 Combine like terms: -3.112244898 + 3.112244898 = 0.000000000 0.000000000 + t = -3.421472851 + 3.112244898 t = -3.421472851 + 3.112244898 Combine like terms: -3.421472851 + 3.112244898 = -0.309227953 t = -0.309227953 Simplifying t = -0.309227953Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.533717749, -0.309227953}
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