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Simplifying 4.9t2 + -8t = 60 Reorder the terms: -8t + 4.9t2 = 60 Solving -8t + 4.9t2 = 60 Solving for variable 't'. Reorder the terms: -60 + -8t + 4.9t2 = 60 + -60 Combine like terms: 60 + -60 = 0 -60 + -8t + 4.9t2 = 0 Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -12.24489796 + -1.632653061t + t2 = 0 Move the constant term to the right: Add '12.24489796' to each side of the equation. -12.24489796 + -1.632653061t + 12.24489796 + t2 = 0 + 12.24489796 Reorder the terms: -12.24489796 + 12.24489796 + -1.632653061t + t2 = 0 + 12.24489796 Combine like terms: -12.24489796 + 12.24489796 = 0.00000000 0.00000000 + -1.632653061t + t2 = 0 + 12.24489796 -1.632653061t + t2 = 0 + 12.24489796 Combine like terms: 0 + 12.24489796 = 12.24489796 -1.632653061t + t2 = 12.24489796 The t term is -1.632653061t. Take half its coefficient (-0.8163265305). Square it (0.6663890044) and add it to both sides. Add '0.6663890044' to each side of the equation. -1.632653061t + 0.6663890044 + t2 = 12.24489796 + 0.6663890044 Reorder the terms: 0.6663890044 + -1.632653061t + t2 = 12.24489796 + 0.6663890044 Combine like terms: 12.24489796 + 0.6663890044 = 12.9112869644 0.6663890044 + -1.632653061t + t2 = 12.9112869644 Factor a perfect square on the left side: (t + -0.8163265305)(t + -0.8163265305) = 12.9112869644 Calculate the square root of the right side: 3.593227931 Break this problem into two subproblems by setting (t + -0.8163265305) equal to 3.593227931 and -3.593227931.Subproblem 1
t + -0.8163265305 = 3.593227931 Simplifying t + -0.8163265305 = 3.593227931 Reorder the terms: -0.8163265305 + t = 3.593227931 Solving -0.8163265305 + t = 3.593227931 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.8163265305' to each side of the equation. -0.8163265305 + 0.8163265305 + t = 3.593227931 + 0.8163265305 Combine like terms: -0.8163265305 + 0.8163265305 = 0.0000000000 0.0000000000 + t = 3.593227931 + 0.8163265305 t = 3.593227931 + 0.8163265305 Combine like terms: 3.593227931 + 0.8163265305 = 4.4095544615 t = 4.4095544615 Simplifying t = 4.4095544615Subproblem 2
t + -0.8163265305 = -3.593227931 Simplifying t + -0.8163265305 = -3.593227931 Reorder the terms: -0.8163265305 + t = -3.593227931 Solving -0.8163265305 + t = -3.593227931 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.8163265305' to each side of the equation. -0.8163265305 + 0.8163265305 + t = -3.593227931 + 0.8163265305 Combine like terms: -0.8163265305 + 0.8163265305 = 0.0000000000 0.0000000000 + t = -3.593227931 + 0.8163265305 t = -3.593227931 + 0.8163265305 Combine like terms: -3.593227931 + 0.8163265305 = -2.7769014005 t = -2.7769014005 Simplifying t = -2.7769014005Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.4095544615, -2.7769014005}
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