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Simplifying 22 = 2 + 44t + -16t2 Solving 22 = 2 + 44t + -16t2 Solving for variable 't'. Combine like terms: 22 + -2 = 20 20 + -44t + 16t2 = 2 + 44t + -16t2 + -2 + -44t + 16t2 Reorder the terms: 20 + -44t + 16t2 = 2 + -2 + 44t + -44t + -16t2 + 16t2 Combine like terms: 2 + -2 = 0 20 + -44t + 16t2 = 0 + 44t + -44t + -16t2 + 16t2 20 + -44t + 16t2 = 44t + -44t + -16t2 + 16t2 Combine like terms: 44t + -44t = 0 20 + -44t + 16t2 = 0 + -16t2 + 16t2 20 + -44t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 20 + -44t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(5 + -11t + 4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(5 + -11t + 4t2)' equal to zero and attempt to solve: Simplifying 5 + -11t + 4t2 = 0 Solving 5 + -11t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.25 + -2.75t + t2 = 0 Move the constant term to the right: Add '-1.25' to each side of the equation. 1.25 + -2.75t + -1.25 + t2 = 0 + -1.25 Reorder the terms: 1.25 + -1.25 + -2.75t + t2 = 0 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + -2.75t + t2 = 0 + -1.25 -2.75t + t2 = 0 + -1.25 Combine like terms: 0 + -1.25 = -1.25 -2.75t + t2 = -1.25 The t term is -2.75t. Take half its coefficient (-1.375). Square it (1.890625) and add it to both sides. Add '1.890625' to each side of the equation. -2.75t + 1.890625 + t2 = -1.25 + 1.890625 Reorder the terms: 1.890625 + -2.75t + t2 = -1.25 + 1.890625 Combine like terms: -1.25 + 1.890625 = 0.640625 1.890625 + -2.75t + t2 = 0.640625 Factor a perfect square on the left side: (t + -1.375)(t + -1.375) = 0.640625 Calculate the square root of the right side: 0.80039053 Break this problem into two subproblems by setting (t + -1.375) equal to 0.80039053 and -0.80039053.Subproblem 1
t + -1.375 = 0.80039053 Simplifying t + -1.375 = 0.80039053 Reorder the terms: -1.375 + t = 0.80039053 Solving -1.375 + t = 0.80039053 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.375' to each side of the equation. -1.375 + 1.375 + t = 0.80039053 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + t = 0.80039053 + 1.375 t = 0.80039053 + 1.375 Combine like terms: 0.80039053 + 1.375 = 2.17539053 t = 2.17539053 Simplifying t = 2.17539053Subproblem 2
t + -1.375 = -0.80039053 Simplifying t + -1.375 = -0.80039053 Reorder the terms: -1.375 + t = -0.80039053 Solving -1.375 + t = -0.80039053 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.375' to each side of the equation. -1.375 + 1.375 + t = -0.80039053 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + t = -0.80039053 + 1.375 t = -0.80039053 + 1.375 Combine like terms: -0.80039053 + 1.375 = 0.57460947 t = 0.57460947 Simplifying t = 0.57460947Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.17539053, 0.57460947}Solution
t = {2.17539053, 0.57460947}
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