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Simplifying 59 = -16t2 + 68t Reorder the terms: 59 = 68t + -16t2 Solving 59 = 68t + -16t2 Solving for variable 't'. Reorder the terms: 59 + -68t + 16t2 = 68t + -68t + -16t2 + 16t2 Combine like terms: 68t + -68t = 0 59 + -68t + 16t2 = 0 + -16t2 + 16t2 59 + -68t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 59 + -68t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 3.6875 + -4.25t + t2 = 0 Move the constant term to the right: Add '-3.6875' to each side of the equation. 3.6875 + -4.25t + -3.6875 + t2 = 0 + -3.6875 Reorder the terms: 3.6875 + -3.6875 + -4.25t + t2 = 0 + -3.6875 Combine like terms: 3.6875 + -3.6875 = 0.0000 0.0000 + -4.25t + t2 = 0 + -3.6875 -4.25t + t2 = 0 + -3.6875 Combine like terms: 0 + -3.6875 = -3.6875 -4.25t + t2 = -3.6875 The t term is -4.25t. Take half its coefficient (-2.125). Square it (4.515625) and add it to both sides. Add '4.515625' to each side of the equation. -4.25t + 4.515625 + t2 = -3.6875 + 4.515625 Reorder the terms: 4.515625 + -4.25t + t2 = -3.6875 + 4.515625 Combine like terms: -3.6875 + 4.515625 = 0.828125 4.515625 + -4.25t + t2 = 0.828125 Factor a perfect square on the left side: (t + -2.125)(t + -2.125) = 0.828125 Calculate the square root of the right side: 0.910013736 Break this problem into two subproblems by setting (t + -2.125) equal to 0.910013736 and -0.910013736.Subproblem 1
t + -2.125 = 0.910013736 Simplifying t + -2.125 = 0.910013736 Reorder the terms: -2.125 + t = 0.910013736 Solving -2.125 + t = 0.910013736 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.125' to each side of the equation. -2.125 + 2.125 + t = 0.910013736 + 2.125 Combine like terms: -2.125 + 2.125 = 0.000 0.000 + t = 0.910013736 + 2.125 t = 0.910013736 + 2.125 Combine like terms: 0.910013736 + 2.125 = 3.035013736 t = 3.035013736 Simplifying t = 3.035013736Subproblem 2
t + -2.125 = -0.910013736 Simplifying t + -2.125 = -0.910013736 Reorder the terms: -2.125 + t = -0.910013736 Solving -2.125 + t = -0.910013736 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.125' to each side of the equation. -2.125 + 2.125 + t = -0.910013736 + 2.125 Combine like terms: -2.125 + 2.125 = 0.000 0.000 + t = -0.910013736 + 2.125 t = -0.910013736 + 2.125 Combine like terms: -0.910013736 + 2.125 = 1.214986264 t = 1.214986264 Simplifying t = 1.214986264Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.035013736, 1.214986264}
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