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Simplifying 0 = -16t2 + 68t + 13 Reorder the terms: 0 = 13 + 68t + -16t2 Solving 0 = 13 + 68t + -16t2 Solving for variable 't'. Combine like terms: 0 + -13 = -13 -13 + -68t + 16t2 = 13 + 68t + -16t2 + -13 + -68t + 16t2 Reorder the terms: -13 + -68t + 16t2 = 13 + -13 + 68t + -68t + -16t2 + 16t2 Combine like terms: 13 + -13 = 0 -13 + -68t + 16t2 = 0 + 68t + -68t + -16t2 + 16t2 -13 + -68t + 16t2 = 68t + -68t + -16t2 + 16t2 Combine like terms: 68t + -68t = 0 -13 + -68t + 16t2 = 0 + -16t2 + 16t2 -13 + -68t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -13 + -68t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.8125 + -4.25t + t2 = 0 Move the constant term to the right: Add '0.8125' to each side of the equation. -0.8125 + -4.25t + 0.8125 + t2 = 0 + 0.8125 Reorder the terms: -0.8125 + 0.8125 + -4.25t + t2 = 0 + 0.8125 Combine like terms: -0.8125 + 0.8125 = 0.0000 0.0000 + -4.25t + t2 = 0 + 0.8125 -4.25t + t2 = 0 + 0.8125 Combine like terms: 0 + 0.8125 = 0.8125 -4.25t + t2 = 0.8125 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 = 0.8125 + 4.515625 Reorder the terms: 4.515625 + -4.25t + t2 = 0.8125 + 4.515625 Combine like terms: 0.8125 + 4.515625 = 5.328125 4.515625 + -4.25t + t2 = 5.328125 Factor a perfect square on the left side: (t + -2.125)(t + -2.125) = 5.328125 Calculate the square root of the right side: 2.308273164 Break this problem into two subproblems by setting (t + -2.125) equal to 2.308273164 and -2.308273164.Subproblem 1
t + -2.125 = 2.308273164 Simplifying t + -2.125 = 2.308273164 Reorder the terms: -2.125 + t = 2.308273164 Solving -2.125 + t = 2.308273164 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 = 2.308273164 + 2.125 Combine like terms: -2.125 + 2.125 = 0.000 0.000 + t = 2.308273164 + 2.125 t = 2.308273164 + 2.125 Combine like terms: 2.308273164 + 2.125 = 4.433273164 t = 4.433273164 Simplifying t = 4.433273164Subproblem 2
t + -2.125 = -2.308273164 Simplifying t + -2.125 = -2.308273164 Reorder the terms: -2.125 + t = -2.308273164 Solving -2.125 + t = -2.308273164 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 = -2.308273164 + 2.125 Combine like terms: -2.125 + 2.125 = 0.000 0.000 + t = -2.308273164 + 2.125 t = -2.308273164 + 2.125 Combine like terms: -2.308273164 + 2.125 = -0.183273164 t = -0.183273164 Simplifying t = -0.183273164Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.433273164, -0.183273164}
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