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Simplifying 0 = -16t2 + 113t + 14 Reorder the terms: 0 = 14 + 113t + -16t2 Solving 0 = 14 + 113t + -16t2 Solving for variable 't'. Combine like terms: 0 + -14 = -14 -14 + -113t + 16t2 = 14 + 113t + -16t2 + -14 + -113t + 16t2 Reorder the terms: -14 + -113t + 16t2 = 14 + -14 + 113t + -113t + -16t2 + 16t2 Combine like terms: 14 + -14 = 0 -14 + -113t + 16t2 = 0 + 113t + -113t + -16t2 + 16t2 -14 + -113t + 16t2 = 113t + -113t + -16t2 + 16t2 Combine like terms: 113t + -113t = 0 -14 + -113t + 16t2 = 0 + -16t2 + 16t2 -14 + -113t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -14 + -113t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.875 + -7.0625t + t2 = 0 Move the constant term to the right: Add '0.875' to each side of the equation. -0.875 + -7.0625t + 0.875 + t2 = 0 + 0.875 Reorder the terms: -0.875 + 0.875 + -7.0625t + t2 = 0 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + -7.0625t + t2 = 0 + 0.875 -7.0625t + t2 = 0 + 0.875 Combine like terms: 0 + 0.875 = 0.875 -7.0625t + t2 = 0.875 The t term is -7.0625t. Take half its coefficient (-3.53125). Square it (12.46972656) and add it to both sides. Add '12.46972656' to each side of the equation. -7.0625t + 12.46972656 + t2 = 0.875 + 12.46972656 Reorder the terms: 12.46972656 + -7.0625t + t2 = 0.875 + 12.46972656 Combine like terms: 0.875 + 12.46972656 = 13.34472656 12.46972656 + -7.0625t + t2 = 13.34472656 Factor a perfect square on the left side: (t + -3.53125)(t + -3.53125) = 13.34472656 Calculate the square root of the right side: 3.653043465 Break this problem into two subproblems by setting (t + -3.53125) equal to 3.653043465 and -3.653043465.Subproblem 1
t + -3.53125 = 3.653043465 Simplifying t + -3.53125 = 3.653043465 Reorder the terms: -3.53125 + t = 3.653043465 Solving -3.53125 + t = 3.653043465 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.53125' to each side of the equation. -3.53125 + 3.53125 + t = 3.653043465 + 3.53125 Combine like terms: -3.53125 + 3.53125 = 0.00000 0.00000 + t = 3.653043465 + 3.53125 t = 3.653043465 + 3.53125 Combine like terms: 3.653043465 + 3.53125 = 7.184293465 t = 7.184293465 Simplifying t = 7.184293465Subproblem 2
t + -3.53125 = -3.653043465 Simplifying t + -3.53125 = -3.653043465 Reorder the terms: -3.53125 + t = -3.653043465 Solving -3.53125 + t = -3.653043465 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.53125' to each side of the equation. -3.53125 + 3.53125 + t = -3.653043465 + 3.53125 Combine like terms: -3.53125 + 3.53125 = 0.00000 0.00000 + t = -3.653043465 + 3.53125 t = -3.653043465 + 3.53125 Combine like terms: -3.653043465 + 3.53125 = -0.121793465 t = -0.121793465 Simplifying t = -0.121793465Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.184293465, -0.121793465}
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