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Simplifying 4.9t2 + -12t + -68 = 0 Reorder the terms: -68 + -12t + 4.9t2 = 0 Solving -68 + -12t + 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'. -13.87755102 + -2.448979592t + t2 = 0 Move the constant term to the right: Add '13.87755102' to each side of the equation. -13.87755102 + -2.448979592t + 13.87755102 + t2 = 0 + 13.87755102 Reorder the terms: -13.87755102 + 13.87755102 + -2.448979592t + t2 = 0 + 13.87755102 Combine like terms: -13.87755102 + 13.87755102 = 0.00000000 0.00000000 + -2.448979592t + t2 = 0 + 13.87755102 -2.448979592t + t2 = 0 + 13.87755102 Combine like terms: 0 + 13.87755102 = 13.87755102 -2.448979592t + t2 = 13.87755102 The t term is -2.448979592t. Take half its coefficient (-1.224489796). Square it (1.499375261) and add it to both sides. Add '1.499375261' to each side of the equation. -2.448979592t + 1.499375261 + t2 = 13.87755102 + 1.499375261 Reorder the terms: 1.499375261 + -2.448979592t + t2 = 13.87755102 + 1.499375261 Combine like terms: 13.87755102 + 1.499375261 = 15.376926281 1.499375261 + -2.448979592t + t2 = 15.376926281 Factor a perfect square on the left side: (t + -1.224489796)(t + -1.224489796) = 15.376926281 Calculate the square root of the right side: 3.921342408 Break this problem into two subproblems by setting (t + -1.224489796) equal to 3.921342408 and -3.921342408.Subproblem 1
t + -1.224489796 = 3.921342408 Simplifying t + -1.224489796 = 3.921342408 Reorder the terms: -1.224489796 + t = 3.921342408 Solving -1.224489796 + t = 3.921342408 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.224489796' to each side of the equation. -1.224489796 + 1.224489796 + t = 3.921342408 + 1.224489796 Combine like terms: -1.224489796 + 1.224489796 = 0.000000000 0.000000000 + t = 3.921342408 + 1.224489796 t = 3.921342408 + 1.224489796 Combine like terms: 3.921342408 + 1.224489796 = 5.145832204 t = 5.145832204 Simplifying t = 5.145832204Subproblem 2
t + -1.224489796 = -3.921342408 Simplifying t + -1.224489796 = -3.921342408 Reorder the terms: -1.224489796 + t = -3.921342408 Solving -1.224489796 + t = -3.921342408 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.224489796' to each side of the equation. -1.224489796 + 1.224489796 + t = -3.921342408 + 1.224489796 Combine like terms: -1.224489796 + 1.224489796 = 0.000000000 0.000000000 + t = -3.921342408 + 1.224489796 t = -3.921342408 + 1.224489796 Combine like terms: -3.921342408 + 1.224489796 = -2.696852612 t = -2.696852612 Simplifying t = -2.696852612Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.145832204, -2.696852612}
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