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Simplifying 5 = -16t2 + 17t + 12 Reorder the terms: 5 = 12 + 17t + -16t2 Solving 5 = 12 + 17t + -16t2 Solving for variable 't'. Combine like terms: 5 + -12 = -7 -7 + -17t + 16t2 = 12 + 17t + -16t2 + -12 + -17t + 16t2 Reorder the terms: -7 + -17t + 16t2 = 12 + -12 + 17t + -17t + -16t2 + 16t2 Combine like terms: 12 + -12 = 0 -7 + -17t + 16t2 = 0 + 17t + -17t + -16t2 + 16t2 -7 + -17t + 16t2 = 17t + -17t + -16t2 + 16t2 Combine like terms: 17t + -17t = 0 -7 + -17t + 16t2 = 0 + -16t2 + 16t2 -7 + -17t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -7 + -17t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.4375 + -1.0625t + t2 = 0 Move the constant term to the right: Add '0.4375' to each side of the equation. -0.4375 + -1.0625t + 0.4375 + t2 = 0 + 0.4375 Reorder the terms: -0.4375 + 0.4375 + -1.0625t + t2 = 0 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + -1.0625t + t2 = 0 + 0.4375 -1.0625t + t2 = 0 + 0.4375 Combine like terms: 0 + 0.4375 = 0.4375 -1.0625t + t2 = 0.4375 The t term is -1.0625t. Take half its coefficient (-0.53125). Square it (0.2822265625) and add it to both sides. Add '0.2822265625' to each side of the equation. -1.0625t + 0.2822265625 + t2 = 0.4375 + 0.2822265625 Reorder the terms: 0.2822265625 + -1.0625t + t2 = 0.4375 + 0.2822265625 Combine like terms: 0.4375 + 0.2822265625 = 0.7197265625 0.2822265625 + -1.0625t + t2 = 0.7197265625 Factor a perfect square on the left side: (t + -0.53125)(t + -0.53125) = 0.7197265625 Calculate the square root of the right side: 0.848366998 Break this problem into two subproblems by setting (t + -0.53125) equal to 0.848366998 and -0.848366998.Subproblem 1
t + -0.53125 = 0.848366998 Simplifying t + -0.53125 = 0.848366998 Reorder the terms: -0.53125 + t = 0.848366998 Solving -0.53125 + t = 0.848366998 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.53125' to each side of the equation. -0.53125 + 0.53125 + t = 0.848366998 + 0.53125 Combine like terms: -0.53125 + 0.53125 = 0.00000 0.00000 + t = 0.848366998 + 0.53125 t = 0.848366998 + 0.53125 Combine like terms: 0.848366998 + 0.53125 = 1.379616998 t = 1.379616998 Simplifying t = 1.379616998Subproblem 2
t + -0.53125 = -0.848366998 Simplifying t + -0.53125 = -0.848366998 Reorder the terms: -0.53125 + t = -0.848366998 Solving -0.53125 + t = -0.848366998 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.53125' to each side of the equation. -0.53125 + 0.53125 + t = -0.848366998 + 0.53125 Combine like terms: -0.53125 + 0.53125 = 0.00000 0.00000 + t = -0.848366998 + 0.53125 t = -0.848366998 + 0.53125 Combine like terms: -0.848366998 + 0.53125 = -0.317116998 t = -0.317116998 Simplifying t = -0.317116998Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.379616998, -0.317116998}
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