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Simplifying -16t2 + -9t + 157 = 0 Reorder the terms: 157 + -9t + -16t2 = 0 Solving 157 + -9t + -16t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -9.8125 + 0.5625t + t2 = 0 Move the constant term to the right: Add '9.8125' to each side of the equation. -9.8125 + 0.5625t + 9.8125 + t2 = 0 + 9.8125 Reorder the terms: -9.8125 + 9.8125 + 0.5625t + t2 = 0 + 9.8125 Combine like terms: -9.8125 + 9.8125 = 0.0000 0.0000 + 0.5625t + t2 = 0 + 9.8125 0.5625t + t2 = 0 + 9.8125 Combine like terms: 0 + 9.8125 = 9.8125 0.5625t + t2 = 9.8125 The t term is 0.5625t. Take half its coefficient (0.28125). Square it (0.0791015625) and add it to both sides. Add '0.0791015625' to each side of the equation. 0.5625t + 0.0791015625 + t2 = 9.8125 + 0.0791015625 Reorder the terms: 0.0791015625 + 0.5625t + t2 = 9.8125 + 0.0791015625 Combine like terms: 9.8125 + 0.0791015625 = 9.8916015625 0.0791015625 + 0.5625t + t2 = 9.8916015625 Factor a perfect square on the left side: (t + 0.28125)(t + 0.28125) = 9.8916015625 Calculate the square root of the right side: 3.145091662 Break this problem into two subproblems by setting (t + 0.28125) equal to 3.145091662 and -3.145091662.Subproblem 1
t + 0.28125 = 3.145091662 Simplifying t + 0.28125 = 3.145091662 Reorder the terms: 0.28125 + t = 3.145091662 Solving 0.28125 + t = 3.145091662 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.28125' to each side of the equation. 0.28125 + -0.28125 + t = 3.145091662 + -0.28125 Combine like terms: 0.28125 + -0.28125 = 0.00000 0.00000 + t = 3.145091662 + -0.28125 t = 3.145091662 + -0.28125 Combine like terms: 3.145091662 + -0.28125 = 2.863841662 t = 2.863841662 Simplifying t = 2.863841662Subproblem 2
t + 0.28125 = -3.145091662 Simplifying t + 0.28125 = -3.145091662 Reorder the terms: 0.28125 + t = -3.145091662 Solving 0.28125 + t = -3.145091662 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.28125' to each side of the equation. 0.28125 + -0.28125 + t = -3.145091662 + -0.28125 Combine like terms: 0.28125 + -0.28125 = 0.00000 0.00000 + t = -3.145091662 + -0.28125 t = -3.145091662 + -0.28125 Combine like terms: -3.145091662 + -0.28125 = -3.426341662 t = -3.426341662 Simplifying t = -3.426341662Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.863841662, -3.426341662}
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