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Simplifying -4.9t2 + -4t + 2.25 = 0 Reorder the terms: 2.25 + -4t + -4.9t2 = 0 Solving 2.25 + -4t + -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'. -0.4591836735 + 0.8163265306t + t2 = 0 Move the constant term to the right: Add '0.4591836735' to each side of the equation. -0.4591836735 + 0.8163265306t + 0.4591836735 + t2 = 0 + 0.4591836735 Reorder the terms: -0.4591836735 + 0.4591836735 + 0.8163265306t + t2 = 0 + 0.4591836735 Combine like terms: -0.4591836735 + 0.4591836735 = 0.0000000000 0.0000000000 + 0.8163265306t + t2 = 0 + 0.4591836735 0.8163265306t + t2 = 0 + 0.4591836735 Combine like terms: 0 + 0.4591836735 = 0.4591836735 0.8163265306t + t2 = 0.4591836735 The t term is 0.8163265306t. Take half its coefficient (0.4081632653). Square it (0.1665972511) and add it to both sides. Add '0.1665972511' to each side of the equation. 0.8163265306t + 0.1665972511 + t2 = 0.4591836735 + 0.1665972511 Reorder the terms: 0.1665972511 + 0.8163265306t + t2 = 0.4591836735 + 0.1665972511 Combine like terms: 0.4591836735 + 0.1665972511 = 0.6257809246 0.1665972511 + 0.8163265306t + t2 = 0.6257809246 Factor a perfect square on the left side: (t + 0.4081632653)(t + 0.4081632653) = 0.6257809246 Calculate the square root of the right side: 0.791063161 Break this problem into two subproblems by setting (t + 0.4081632653) equal to 0.791063161 and -0.791063161.Subproblem 1
t + 0.4081632653 = 0.791063161 Simplifying t + 0.4081632653 = 0.791063161 Reorder the terms: 0.4081632653 + t = 0.791063161 Solving 0.4081632653 + t = 0.791063161 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.4081632653' to each side of the equation. 0.4081632653 + -0.4081632653 + t = 0.791063161 + -0.4081632653 Combine like terms: 0.4081632653 + -0.4081632653 = 0.0000000000 0.0000000000 + t = 0.791063161 + -0.4081632653 t = 0.791063161 + -0.4081632653 Combine like terms: 0.791063161 + -0.4081632653 = 0.3828998957 t = 0.3828998957 Simplifying t = 0.3828998957Subproblem 2
t + 0.4081632653 = -0.791063161 Simplifying t + 0.4081632653 = -0.791063161 Reorder the terms: 0.4081632653 + t = -0.791063161 Solving 0.4081632653 + t = -0.791063161 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.4081632653' to each side of the equation. 0.4081632653 + -0.4081632653 + t = -0.791063161 + -0.4081632653 Combine like terms: 0.4081632653 + -0.4081632653 = 0.0000000000 0.0000000000 + t = -0.791063161 + -0.4081632653 t = -0.791063161 + -0.4081632653 Combine like terms: -0.791063161 + -0.4081632653 = -1.1992264263 t = -1.1992264263 Simplifying t = -1.1992264263Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.3828998957, -1.1992264263}
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