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Simplifying 4.9t2 + -225t + 620 = 0 Reorder the terms: 620 + -225t + 4.9t2 = 0 Solving 620 + -225t + 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'. 126.5306122 + -45.91836735t + t2 = 0 Move the constant term to the right: Add '-126.5306122' to each side of the equation. 126.5306122 + -45.91836735t + -126.5306122 + t2 = 0 + -126.5306122 Reorder the terms: 126.5306122 + -126.5306122 + -45.91836735t + t2 = 0 + -126.5306122 Combine like terms: 126.5306122 + -126.5306122 = 0.0000000 0.0000000 + -45.91836735t + t2 = 0 + -126.5306122 -45.91836735t + t2 = 0 + -126.5306122 Combine like terms: 0 + -126.5306122 = -126.5306122 -45.91836735t + t2 = -126.5306122 The t term is -45.91836735t. Take half its coefficient (-22.95918368). Square it (527.1241153) and add it to both sides. Add '527.1241153' to each side of the equation. -45.91836735t + 527.1241153 + t2 = -126.5306122 + 527.1241153 Reorder the terms: 527.1241153 + -45.91836735t + t2 = -126.5306122 + 527.1241153 Combine like terms: -126.5306122 + 527.1241153 = 400.5935031 527.1241153 + -45.91836735t + t2 = 400.5935031 Factor a perfect square on the left side: (t + -22.95918368)(t + -22.95918368) = 400.5935031 Calculate the square root of the right side: 20.014832078 Break this problem into two subproblems by setting (t + -22.95918368) equal to 20.014832078 and -20.014832078.Subproblem 1
t + -22.95918368 = 20.014832078 Simplifying t + -22.95918368 = 20.014832078 Reorder the terms: -22.95918368 + t = 20.014832078 Solving -22.95918368 + t = 20.014832078 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '22.95918368' to each side of the equation. -22.95918368 + 22.95918368 + t = 20.014832078 + 22.95918368 Combine like terms: -22.95918368 + 22.95918368 = 0.00000000 0.00000000 + t = 20.014832078 + 22.95918368 t = 20.014832078 + 22.95918368 Combine like terms: 20.014832078 + 22.95918368 = 42.974015758 t = 42.974015758 Simplifying t = 42.974015758Subproblem 2
t + -22.95918368 = -20.014832078 Simplifying t + -22.95918368 = -20.014832078 Reorder the terms: -22.95918368 + t = -20.014832078 Solving -22.95918368 + t = -20.014832078 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '22.95918368' to each side of the equation. -22.95918368 + 22.95918368 + t = -20.014832078 + 22.95918368 Combine like terms: -22.95918368 + 22.95918368 = 0.00000000 0.00000000 + t = -20.014832078 + 22.95918368 t = -20.014832078 + 22.95918368 Combine like terms: -20.014832078 + 22.95918368 = 2.944351602 t = 2.944351602 Simplifying t = 2.944351602Solution
The solution to the problem is based on the solutions from the subproblems. t = {42.974015758, 2.944351602}
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