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Simplifying 0.0795t2 + -0.898t + 1.804 = 0 Reorder the terms: 1.804 + -0.898t + 0.0795t2 = 0 Solving 1.804 + -0.898t + 0.0795t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 0.0795 the coefficient of the squared term: Divide each side by '0.0795'. 22.6918239 + -11.29559748t + t2 = 0 Move the constant term to the right: Add '-22.6918239' to each side of the equation. 22.6918239 + -11.29559748t + -22.6918239 + t2 = 0 + -22.6918239 Reorder the terms: 22.6918239 + -22.6918239 + -11.29559748t + t2 = 0 + -22.6918239 Combine like terms: 22.6918239 + -22.6918239 = 0.0000000 0.0000000 + -11.29559748t + t2 = 0 + -22.6918239 -11.29559748t + t2 = 0 + -22.6918239 Combine like terms: 0 + -22.6918239 = -22.6918239 -11.29559748t + t2 = -22.6918239 The t term is -11.29559748t. Take half its coefficient (-5.64779874). Square it (31.89763061) and add it to both sides. Add '31.89763061' to each side of the equation. -11.29559748t + 31.89763061 + t2 = -22.6918239 + 31.89763061 Reorder the terms: 31.89763061 + -11.29559748t + t2 = -22.6918239 + 31.89763061 Combine like terms: -22.6918239 + 31.89763061 = 9.20580671 31.89763061 + -11.29559748t + t2 = 9.20580671 Factor a perfect square on the left side: (t + -5.64779874)(t + -5.64779874) = 9.20580671 Calculate the square root of the right side: 3.034107234 Break this problem into two subproblems by setting (t + -5.64779874) equal to 3.034107234 and -3.034107234.Subproblem 1
t + -5.64779874 = 3.034107234 Simplifying t + -5.64779874 = 3.034107234 Reorder the terms: -5.64779874 + t = 3.034107234 Solving -5.64779874 + t = 3.034107234 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.64779874' to each side of the equation. -5.64779874 + 5.64779874 + t = 3.034107234 + 5.64779874 Combine like terms: -5.64779874 + 5.64779874 = 0.00000000 0.00000000 + t = 3.034107234 + 5.64779874 t = 3.034107234 + 5.64779874 Combine like terms: 3.034107234 + 5.64779874 = 8.681905974 t = 8.681905974 Simplifying t = 8.681905974Subproblem 2
t + -5.64779874 = -3.034107234 Simplifying t + -5.64779874 = -3.034107234 Reorder the terms: -5.64779874 + t = -3.034107234 Solving -5.64779874 + t = -3.034107234 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.64779874' to each side of the equation. -5.64779874 + 5.64779874 + t = -3.034107234 + 5.64779874 Combine like terms: -5.64779874 + 5.64779874 = 0.00000000 0.00000000 + t = -3.034107234 + 5.64779874 t = -3.034107234 + 5.64779874 Combine like terms: -3.034107234 + 5.64779874 = 2.613691506 t = 2.613691506 Simplifying t = 2.613691506Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.681905974, 2.613691506}
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