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Simplifying -16t2 + -151t + -88 = 0 Reorder the terms: -88 + -151t + -16t2 = 0 Solving -88 + -151t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '-1'. -1(88 + 151t + 16t2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(88 + 151t + 16t2)' equal to zero and attempt to solve: Simplifying 88 + 151t + 16t2 = 0 Solving 88 + 151t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 5.5 + 9.4375t + t2 = 0 Move the constant term to the right: Add '-5.5' to each side of the equation. 5.5 + 9.4375t + -5.5 + t2 = 0 + -5.5 Reorder the terms: 5.5 + -5.5 + 9.4375t + t2 = 0 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + 9.4375t + t2 = 0 + -5.5 9.4375t + t2 = 0 + -5.5 Combine like terms: 0 + -5.5 = -5.5 9.4375t + t2 = -5.5 The t term is 9.4375t. Take half its coefficient (4.71875). Square it (22.26660156) and add it to both sides. Add '22.26660156' to each side of the equation. 9.4375t + 22.26660156 + t2 = -5.5 + 22.26660156 Reorder the terms: 22.26660156 + 9.4375t + t2 = -5.5 + 22.26660156 Combine like terms: -5.5 + 22.26660156 = 16.76660156 22.26660156 + 9.4375t + t2 = 16.76660156 Factor a perfect square on the left side: (t + 4.71875)(t + 4.71875) = 16.76660156 Calculate the square root of the right side: 4.094704087 Break this problem into two subproblems by setting (t + 4.71875) equal to 4.094704087 and -4.094704087.Subproblem 1
t + 4.71875 = 4.094704087 Simplifying t + 4.71875 = 4.094704087 Reorder the terms: 4.71875 + t = 4.094704087 Solving 4.71875 + t = 4.094704087 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-4.71875' to each side of the equation. 4.71875 + -4.71875 + t = 4.094704087 + -4.71875 Combine like terms: 4.71875 + -4.71875 = 0.00000 0.00000 + t = 4.094704087 + -4.71875 t = 4.094704087 + -4.71875 Combine like terms: 4.094704087 + -4.71875 = -0.624045913 t = -0.624045913 Simplifying t = -0.624045913Subproblem 2
t + 4.71875 = -4.094704087 Simplifying t + 4.71875 = -4.094704087 Reorder the terms: 4.71875 + t = -4.094704087 Solving 4.71875 + t = -4.094704087 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-4.71875' to each side of the equation. 4.71875 + -4.71875 + t = -4.094704087 + -4.71875 Combine like terms: 4.71875 + -4.71875 = 0.00000 0.00000 + t = -4.094704087 + -4.71875 t = -4.094704087 + -4.71875 Combine like terms: -4.094704087 + -4.71875 = -8.813454087 t = -8.813454087 Simplifying t = -8.813454087Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.624045913, -8.813454087}Solution
t = {-0.624045913, -8.813454087}
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