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Simplifying 0 = 6 + 34t + -16t2 Solving 0 = 6 + 34t + -16t2 Solving for variable 't'. Combine like terms: 0 + -6 = -6 -6 + -34t + 16t2 = 6 + 34t + -16t2 + -6 + -34t + 16t2 Reorder the terms: -6 + -34t + 16t2 = 6 + -6 + 34t + -34t + -16t2 + 16t2 Combine like terms: 6 + -6 = 0 -6 + -34t + 16t2 = 0 + 34t + -34t + -16t2 + 16t2 -6 + -34t + 16t2 = 34t + -34t + -16t2 + 16t2 Combine like terms: 34t + -34t = 0 -6 + -34t + 16t2 = 0 + -16t2 + 16t2 -6 + -34t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -6 + -34t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + -17t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + -17t + 8t2)' equal to zero and attempt to solve: Simplifying -3 + -17t + 8t2 = 0 Solving -3 + -17t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.375 + -2.125t + t2 = 0 Move the constant term to the right: Add '0.375' to each side of the equation. -0.375 + -2.125t + 0.375 + t2 = 0 + 0.375 Reorder the terms: -0.375 + 0.375 + -2.125t + t2 = 0 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + -2.125t + t2 = 0 + 0.375 -2.125t + t2 = 0 + 0.375 Combine like terms: 0 + 0.375 = 0.375 -2.125t + t2 = 0.375 The t term is -2.125t. Take half its coefficient (-1.0625). Square it (1.12890625) and add it to both sides. Add '1.12890625' to each side of the equation. -2.125t + 1.12890625 + t2 = 0.375 + 1.12890625 Reorder the terms: 1.12890625 + -2.125t + t2 = 0.375 + 1.12890625 Combine like terms: 0.375 + 1.12890625 = 1.50390625 1.12890625 + -2.125t + t2 = 1.50390625 Factor a perfect square on the left side: (t + -1.0625)(t + -1.0625) = 1.50390625 Calculate the square root of the right side: 1.226338554 Break this problem into two subproblems by setting (t + -1.0625) equal to 1.226338554 and -1.226338554.Subproblem 1
t + -1.0625 = 1.226338554 Simplifying t + -1.0625 = 1.226338554 Reorder the terms: -1.0625 + t = 1.226338554 Solving -1.0625 + t = 1.226338554 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.0625' to each side of the equation. -1.0625 + 1.0625 + t = 1.226338554 + 1.0625 Combine like terms: -1.0625 + 1.0625 = 0.0000 0.0000 + t = 1.226338554 + 1.0625 t = 1.226338554 + 1.0625 Combine like terms: 1.226338554 + 1.0625 = 2.288838554 t = 2.288838554 Simplifying t = 2.288838554Subproblem 2
t + -1.0625 = -1.226338554 Simplifying t + -1.0625 = -1.226338554 Reorder the terms: -1.0625 + t = -1.226338554 Solving -1.0625 + t = -1.226338554 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.0625' to each side of the equation. -1.0625 + 1.0625 + t = -1.226338554 + 1.0625 Combine like terms: -1.0625 + 1.0625 = 0.0000 0.0000 + t = -1.226338554 + 1.0625 t = -1.226338554 + 1.0625 Combine like terms: -1.226338554 + 1.0625 = -0.163838554 t = -0.163838554 Simplifying t = -0.163838554Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.288838554, -0.163838554}Solution
t = {2.288838554, -0.163838554}
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