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Simplifying -16t2 + -2t + 20 = 0 Reorder the terms: 20 + -2t + -16t2 = 0 Solving 20 + -2t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(10 + -1t + -8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(10 + -1t + -8t2)' equal to zero and attempt to solve: Simplifying 10 + -1t + -8t2 = 0 Solving 10 + -1t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -1.25 + 0.125t + t2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + 0.125t + 1.25 + t2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + 0.125t + t2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + 0.125t + t2 = 0 + 1.25 0.125t + t2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 0.125t + t2 = 1.25 The t term is 0.125t. Take half its coefficient (0.0625). Square it (0.00390625) and add it to both sides. Add '0.00390625' to each side of the equation. 0.125t + 0.00390625 + t2 = 1.25 + 0.00390625 Reorder the terms: 0.00390625 + 0.125t + t2 = 1.25 + 0.00390625 Combine like terms: 1.25 + 0.00390625 = 1.25390625 0.00390625 + 0.125t + t2 = 1.25390625 Factor a perfect square on the left side: (t + 0.0625)(t + 0.0625) = 1.25390625 Calculate the square root of the right side: 1.119779554 Break this problem into two subproblems by setting (t + 0.0625) equal to 1.119779554 and -1.119779554.Subproblem 1
t + 0.0625 = 1.119779554 Simplifying t + 0.0625 = 1.119779554 Reorder the terms: 0.0625 + t = 1.119779554 Solving 0.0625 + t = 1.119779554 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.0625' to each side of the equation. 0.0625 + -0.0625 + t = 1.119779554 + -0.0625 Combine like terms: 0.0625 + -0.0625 = 0.0000 0.0000 + t = 1.119779554 + -0.0625 t = 1.119779554 + -0.0625 Combine like terms: 1.119779554 + -0.0625 = 1.057279554 t = 1.057279554 Simplifying t = 1.057279554Subproblem 2
t + 0.0625 = -1.119779554 Simplifying t + 0.0625 = -1.119779554 Reorder the terms: 0.0625 + t = -1.119779554 Solving 0.0625 + t = -1.119779554 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.0625' to each side of the equation. 0.0625 + -0.0625 + t = -1.119779554 + -0.0625 Combine like terms: 0.0625 + -0.0625 = 0.0000 0.0000 + t = -1.119779554 + -0.0625 t = -1.119779554 + -0.0625 Combine like terms: -1.119779554 + -0.0625 = -1.182279554 t = -1.182279554 Simplifying t = -1.182279554Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.057279554, -1.182279554}Solution
t = {1.057279554, -1.182279554}
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