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Simplifying 60 + 11t + -4.9t2 = 0 Solving 60 + 11t + -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'. -12.24489796 + -2.244897959t + t2 = 0 Move the constant term to the right: Add '12.24489796' to each side of the equation. -12.24489796 + -2.244897959t + 12.24489796 + t2 = 0 + 12.24489796 Reorder the terms: -12.24489796 + 12.24489796 + -2.244897959t + t2 = 0 + 12.24489796 Combine like terms: -12.24489796 + 12.24489796 = 0.00000000 0.00000000 + -2.244897959t + t2 = 0 + 12.24489796 -2.244897959t + t2 = 0 + 12.24489796 Combine like terms: 0 + 12.24489796 = 12.24489796 -2.244897959t + t2 = 12.24489796 The t term is -2.244897959t. Take half its coefficient (-1.12244898). Square it (1.259891713) and add it to both sides. Add '1.259891713' to each side of the equation. -2.244897959t + 1.259891713 + t2 = 12.24489796 + 1.259891713 Reorder the terms: 1.259891713 + -2.244897959t + t2 = 12.24489796 + 1.259891713 Combine like terms: 12.24489796 + 1.259891713 = 13.504789673 1.259891713 + -2.244897959t + t2 = 13.504789673 Factor a perfect square on the left side: (t + -1.12244898)(t + -1.12244898) = 13.504789673 Calculate the square root of the right side: 3.674886348 Break this problem into two subproblems by setting (t + -1.12244898) equal to 3.674886348 and -3.674886348.Subproblem 1
t + -1.12244898 = 3.674886348 Simplifying t + -1.12244898 = 3.674886348 Reorder the terms: -1.12244898 + t = 3.674886348 Solving -1.12244898 + t = 3.674886348 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.12244898' to each side of the equation. -1.12244898 + 1.12244898 + t = 3.674886348 + 1.12244898 Combine like terms: -1.12244898 + 1.12244898 = 0.00000000 0.00000000 + t = 3.674886348 + 1.12244898 t = 3.674886348 + 1.12244898 Combine like terms: 3.674886348 + 1.12244898 = 4.797335328 t = 4.797335328 Simplifying t = 4.797335328Subproblem 2
t + -1.12244898 = -3.674886348 Simplifying t + -1.12244898 = -3.674886348 Reorder the terms: -1.12244898 + t = -3.674886348 Solving -1.12244898 + t = -3.674886348 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.12244898' to each side of the equation. -1.12244898 + 1.12244898 + t = -3.674886348 + 1.12244898 Combine like terms: -1.12244898 + 1.12244898 = 0.00000000 0.00000000 + t = -3.674886348 + 1.12244898 t = -3.674886348 + 1.12244898 Combine like terms: -3.674886348 + 1.12244898 = -2.552437368 t = -2.552437368 Simplifying t = -2.552437368Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.797335328, -2.552437368}
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