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Simplifying 16t2 + -32t = 18 Reorder the terms: -32t + 16t2 = 18 Solving -32t + 16t2 = 18 Solving for variable 't'. Reorder the terms: -18 + -32t + 16t2 = 18 + -18 Combine like terms: 18 + -18 = 0 -18 + -32t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-9 + -16t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-9 + -16t + 8t2)' equal to zero and attempt to solve: Simplifying -9 + -16t + 8t2 = 0 Solving -9 + -16t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -1.125 + -2t + t2 = 0 Move the constant term to the right: Add '1.125' to each side of the equation. -1.125 + -2t + 1.125 + t2 = 0 + 1.125 Reorder the terms: -1.125 + 1.125 + -2t + t2 = 0 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + -2t + t2 = 0 + 1.125 -2t + t2 = 0 + 1.125 Combine like terms: 0 + 1.125 = 1.125 -2t + t2 = 1.125 The t term is -2t. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2t + 1 + t2 = 1.125 + 1 Reorder the terms: 1 + -2t + t2 = 1.125 + 1 Combine like terms: 1.125 + 1 = 2.125 1 + -2t + t2 = 2.125 Factor a perfect square on the left side: (t + -1)(t + -1) = 2.125 Calculate the square root of the right side: 1.457737974 Break this problem into two subproblems by setting (t + -1) equal to 1.457737974 and -1.457737974.Subproblem 1
t + -1 = 1.457737974 Simplifying t + -1 = 1.457737974 Reorder the terms: -1 + t = 1.457737974 Solving -1 + t = 1.457737974 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + t = 1.457737974 + 1 Combine like terms: -1 + 1 = 0 0 + t = 1.457737974 + 1 t = 1.457737974 + 1 Combine like terms: 1.457737974 + 1 = 2.457737974 t = 2.457737974 Simplifying t = 2.457737974Subproblem 2
t + -1 = -1.457737974 Simplifying t + -1 = -1.457737974 Reorder the terms: -1 + t = -1.457737974 Solving -1 + t = -1.457737974 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + t = -1.457737974 + 1 Combine like terms: -1 + 1 = 0 0 + t = -1.457737974 + 1 t = -1.457737974 + 1 Combine like terms: -1.457737974 + 1 = -0.457737974 t = -0.457737974 Simplifying t = -0.457737974Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.457737974, -0.457737974}Solution
t = {2.457737974, -0.457737974}
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