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Simplifying 4.8t2 + 58t + 10 = 0 Reorder the terms: 10 + 58t + 4.8t2 = 0 Solving 10 + 58t + 4.8t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 4.8 the coefficient of the squared term: Divide each side by '4.8'. 2.083333333 + 12.08333333t + t2 = 0 Move the constant term to the right: Add '-2.083333333' to each side of the equation. 2.083333333 + 12.08333333t + -2.083333333 + t2 = 0 + -2.083333333 Reorder the terms: 2.083333333 + -2.083333333 + 12.08333333t + t2 = 0 + -2.083333333 Combine like terms: 2.083333333 + -2.083333333 = 0.000000000 0.000000000 + 12.08333333t + t2 = 0 + -2.083333333 12.08333333t + t2 = 0 + -2.083333333 Combine like terms: 0 + -2.083333333 = -2.083333333 12.08333333t + t2 = -2.083333333 The t term is 12.08333333t. Take half its coefficient (6.041666665). Square it (36.50173609) and add it to both sides. Add '36.50173609' to each side of the equation. 12.08333333t + 36.50173609 + t2 = -2.083333333 + 36.50173609 Reorder the terms: 36.50173609 + 12.08333333t + t2 = -2.083333333 + 36.50173609 Combine like terms: -2.083333333 + 36.50173609 = 34.418402757 36.50173609 + 12.08333333t + t2 = 34.418402757 Factor a perfect square on the left side: (t + 6.041666665)(t + 6.041666665) = 34.418402757 Calculate the square root of the right side: 5.866719932 Break this problem into two subproblems by setting (t + 6.041666665) equal to 5.866719932 and -5.866719932.Subproblem 1
t + 6.041666665 = 5.866719932 Simplifying t + 6.041666665 = 5.866719932 Reorder the terms: 6.041666665 + t = 5.866719932 Solving 6.041666665 + t = 5.866719932 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-6.041666665' to each side of the equation. 6.041666665 + -6.041666665 + t = 5.866719932 + -6.041666665 Combine like terms: 6.041666665 + -6.041666665 = 0.000000000 0.000000000 + t = 5.866719932 + -6.041666665 t = 5.866719932 + -6.041666665 Combine like terms: 5.866719932 + -6.041666665 = -0.174946733 t = -0.174946733 Simplifying t = -0.174946733Subproblem 2
t + 6.041666665 = -5.866719932 Simplifying t + 6.041666665 = -5.866719932 Reorder the terms: 6.041666665 + t = -5.866719932 Solving 6.041666665 + t = -5.866719932 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-6.041666665' to each side of the equation. 6.041666665 + -6.041666665 + t = -5.866719932 + -6.041666665 Combine like terms: 6.041666665 + -6.041666665 = 0.000000000 0.000000000 + t = -5.866719932 + -6.041666665 t = -5.866719932 + -6.041666665 Combine like terms: -5.866719932 + -6.041666665 = -11.908386597 t = -11.908386597 Simplifying t = -11.908386597Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.174946733, -11.908386597}
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