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Simplifying 0 = -16t2 + 146t + 20 Reorder the terms: 0 = 20 + 146t + -16t2 Solving 0 = 20 + 146t + -16t2 Solving for variable 't'. Combine like terms: 0 + -20 = -20 -20 + -146t + 16t2 = 20 + 146t + -16t2 + -20 + -146t + 16t2 Reorder the terms: -20 + -146t + 16t2 = 20 + -20 + 146t + -146t + -16t2 + 16t2 Combine like terms: 20 + -20 = 0 -20 + -146t + 16t2 = 0 + 146t + -146t + -16t2 + 16t2 -20 + -146t + 16t2 = 146t + -146t + -16t2 + 16t2 Combine like terms: 146t + -146t = 0 -20 + -146t + 16t2 = 0 + -16t2 + 16t2 -20 + -146t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -20 + -146t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-10 + -73t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-10 + -73t + 8t2)' equal to zero and attempt to solve: Simplifying -10 + -73t + 8t2 = 0 Solving -10 + -73t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -1.25 + -9.125t + t2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + -9.125t + 1.25 + t2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + -9.125t + t2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + -9.125t + t2 = 0 + 1.25 -9.125t + t2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 -9.125t + t2 = 1.25 The t term is -9.125t. Take half its coefficient (-4.5625). Square it (20.81640625) and add it to both sides. Add '20.81640625' to each side of the equation. -9.125t + 20.81640625 + t2 = 1.25 + 20.81640625 Reorder the terms: 20.81640625 + -9.125t + t2 = 1.25 + 20.81640625 Combine like terms: 1.25 + 20.81640625 = 22.06640625 20.81640625 + -9.125t + t2 = 22.06640625 Factor a perfect square on the left side: (t + -4.5625)(t + -4.5625) = 22.06640625 Calculate the square root of the right side: 4.697489356 Break this problem into two subproblems by setting (t + -4.5625) equal to 4.697489356 and -4.697489356.Subproblem 1
t + -4.5625 = 4.697489356 Simplifying t + -4.5625 = 4.697489356 Reorder the terms: -4.5625 + t = 4.697489356 Solving -4.5625 + t = 4.697489356 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.5625' to each side of the equation. -4.5625 + 4.5625 + t = 4.697489356 + 4.5625 Combine like terms: -4.5625 + 4.5625 = 0.0000 0.0000 + t = 4.697489356 + 4.5625 t = 4.697489356 + 4.5625 Combine like terms: 4.697489356 + 4.5625 = 9.259989356 t = 9.259989356 Simplifying t = 9.259989356Subproblem 2
t + -4.5625 = -4.697489356 Simplifying t + -4.5625 = -4.697489356 Reorder the terms: -4.5625 + t = -4.697489356 Solving -4.5625 + t = -4.697489356 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.5625' to each side of the equation. -4.5625 + 4.5625 + t = -4.697489356 + 4.5625 Combine like terms: -4.5625 + 4.5625 = 0.0000 0.0000 + t = -4.697489356 + 4.5625 t = -4.697489356 + 4.5625 Combine like terms: -4.697489356 + 4.5625 = -0.134989356 t = -0.134989356 Simplifying t = -0.134989356Solution
The solution to the problem is based on the solutions from the subproblems. t = {9.259989356, -0.134989356}Solution
t = {9.259989356, -0.134989356}
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