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Simplifying 0 = -16t2 + 10t + 1.3 Reorder the terms: 0 = 1.3 + 10t + -16t2 Solving 0 = 1.3 + 10t + -16t2 Solving for variable 't'. Combine like terms: 0 + -1.3 = -1.3 -1.3 + -10t + 16t2 = 1.3 + 10t + -16t2 + -1.3 + -10t + 16t2 Reorder the terms: -1.3 + -10t + 16t2 = 1.3 + -1.3 + 10t + -10t + -16t2 + 16t2 Combine like terms: 1.3 + -1.3 = 0.0 -1.3 + -10t + 16t2 = 0.0 + 10t + -10t + -16t2 + 16t2 -1.3 + -10t + 16t2 = 10t + -10t + -16t2 + 16t2 Combine like terms: 10t + -10t = 0 -1.3 + -10t + 16t2 = 0 + -16t2 + 16t2 -1.3 + -10t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -1.3 + -10t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.08125 + -0.625t + t2 = 0 Move the constant term to the right: Add '0.08125' to each side of the equation. -0.08125 + -0.625t + 0.08125 + t2 = 0 + 0.08125 Reorder the terms: -0.08125 + 0.08125 + -0.625t + t2 = 0 + 0.08125 Combine like terms: -0.08125 + 0.08125 = 0.00000 0.00000 + -0.625t + t2 = 0 + 0.08125 -0.625t + t2 = 0 + 0.08125 Combine like terms: 0 + 0.08125 = 0.08125 -0.625t + t2 = 0.08125 The t term is -0.625t. Take half its coefficient (-0.3125). Square it (0.09765625) and add it to both sides. Add '0.09765625' to each side of the equation. -0.625t + 0.09765625 + t2 = 0.08125 + 0.09765625 Reorder the terms: 0.09765625 + -0.625t + t2 = 0.08125 + 0.09765625 Combine like terms: 0.08125 + 0.09765625 = 0.17890625 0.09765625 + -0.625t + t2 = 0.17890625 Factor a perfect square on the left side: (t + -0.3125)(t + -0.3125) = 0.17890625 Calculate the square root of the right side: 0.422973108 Break this problem into two subproblems by setting (t + -0.3125) equal to 0.422973108 and -0.422973108.Subproblem 1
t + -0.3125 = 0.422973108 Simplifying t + -0.3125 = 0.422973108 Reorder the terms: -0.3125 + t = 0.422973108 Solving -0.3125 + t = 0.422973108 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.3125' to each side of the equation. -0.3125 + 0.3125 + t = 0.422973108 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + t = 0.422973108 + 0.3125 t = 0.422973108 + 0.3125 Combine like terms: 0.422973108 + 0.3125 = 0.735473108 t = 0.735473108 Simplifying t = 0.735473108Subproblem 2
t + -0.3125 = -0.422973108 Simplifying t + -0.3125 = -0.422973108 Reorder the terms: -0.3125 + t = -0.422973108 Solving -0.3125 + t = -0.422973108 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.3125' to each side of the equation. -0.3125 + 0.3125 + t = -0.422973108 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + t = -0.422973108 + 0.3125 t = -0.422973108 + 0.3125 Combine like terms: -0.422973108 + 0.3125 = -0.110473108 t = -0.110473108 Simplifying t = -0.110473108Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.735473108, -0.110473108}
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