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Simplifying -16t2 + 161t + 57 = 0 Reorder the terms: 57 + 161t + -16t2 = 0 Solving 57 + 161t + -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'. -3.5625 + -10.0625t + t2 = 0 Move the constant term to the right: Add '3.5625' to each side of the equation. -3.5625 + -10.0625t + 3.5625 + t2 = 0 + 3.5625 Reorder the terms: -3.5625 + 3.5625 + -10.0625t + t2 = 0 + 3.5625 Combine like terms: -3.5625 + 3.5625 = 0.0000 0.0000 + -10.0625t + t2 = 0 + 3.5625 -10.0625t + t2 = 0 + 3.5625 Combine like terms: 0 + 3.5625 = 3.5625 -10.0625t + t2 = 3.5625 The t term is -10.0625t. Take half its coefficient (-5.03125). Square it (25.31347656) and add it to both sides. Add '25.31347656' to each side of the equation. -10.0625t + 25.31347656 + t2 = 3.5625 + 25.31347656 Reorder the terms: 25.31347656 + -10.0625t + t2 = 3.5625 + 25.31347656 Combine like terms: 3.5625 + 25.31347656 = 28.87597656 25.31347656 + -10.0625t + t2 = 28.87597656 Factor a perfect square on the left side: (t + -5.03125)(t + -5.03125) = 28.87597656 Calculate the square root of the right side: 5.373637182 Break this problem into two subproblems by setting (t + -5.03125) equal to 5.373637182 and -5.373637182.Subproblem 1
t + -5.03125 = 5.373637182 Simplifying t + -5.03125 = 5.373637182 Reorder the terms: -5.03125 + t = 5.373637182 Solving -5.03125 + t = 5.373637182 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.03125' to each side of the equation. -5.03125 + 5.03125 + t = 5.373637182 + 5.03125 Combine like terms: -5.03125 + 5.03125 = 0.00000 0.00000 + t = 5.373637182 + 5.03125 t = 5.373637182 + 5.03125 Combine like terms: 5.373637182 + 5.03125 = 10.404887182 t = 10.404887182 Simplifying t = 10.404887182Subproblem 2
t + -5.03125 = -5.373637182 Simplifying t + -5.03125 = -5.373637182 Reorder the terms: -5.03125 + t = -5.373637182 Solving -5.03125 + t = -5.373637182 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.03125' to each side of the equation. -5.03125 + 5.03125 + t = -5.373637182 + 5.03125 Combine like terms: -5.03125 + 5.03125 = 0.00000 0.00000 + t = -5.373637182 + 5.03125 t = -5.373637182 + 5.03125 Combine like terms: -5.373637182 + 5.03125 = -0.342387182 t = -0.342387182 Simplifying t = -0.342387182Solution
The solution to the problem is based on the solutions from the subproblems. t = {10.404887182, -0.342387182}
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