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Simplifying 0 = -16t2 + 32t + 58 Reorder the terms: 0 = 58 + 32t + -16t2 Solving 0 = 58 + 32t + -16t2 Solving for variable 't'. Combine like terms: 0 + -58 = -58 -58 + -32t + 16t2 = 58 + 32t + -16t2 + -58 + -32t + 16t2 Reorder the terms: -58 + -32t + 16t2 = 58 + -58 + 32t + -32t + -16t2 + 16t2 Combine like terms: 58 + -58 = 0 -58 + -32t + 16t2 = 0 + 32t + -32t + -16t2 + 16t2 -58 + -32t + 16t2 = 32t + -32t + -16t2 + 16t2 Combine like terms: 32t + -32t = 0 -58 + -32t + 16t2 = 0 + -16t2 + 16t2 -58 + -32t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -58 + -32t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-29 + -16t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-29 + -16t + 8t2)' equal to zero and attempt to solve: Simplifying -29 + -16t + 8t2 = 0 Solving -29 + -16t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -3.625 + -2t + t2 = 0 Move the constant term to the right: Add '3.625' to each side of the equation. -3.625 + -2t + 3.625 + t2 = 0 + 3.625 Reorder the terms: -3.625 + 3.625 + -2t + t2 = 0 + 3.625 Combine like terms: -3.625 + 3.625 = 0.000 0.000 + -2t + t2 = 0 + 3.625 -2t + t2 = 0 + 3.625 Combine like terms: 0 + 3.625 = 3.625 -2t + t2 = 3.625 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 = 3.625 + 1 Reorder the terms: 1 + -2t + t2 = 3.625 + 1 Combine like terms: 3.625 + 1 = 4.625 1 + -2t + t2 = 4.625 Factor a perfect square on the left side: (t + -1)(t + -1) = 4.625 Calculate the square root of the right side: 2.150581317 Break this problem into two subproblems by setting (t + -1) equal to 2.150581317 and -2.150581317.Subproblem 1
t + -1 = 2.150581317 Simplifying t + -1 = 2.150581317 Reorder the terms: -1 + t = 2.150581317 Solving -1 + t = 2.150581317 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 = 2.150581317 + 1 Combine like terms: -1 + 1 = 0 0 + t = 2.150581317 + 1 t = 2.150581317 + 1 Combine like terms: 2.150581317 + 1 = 3.150581317 t = 3.150581317 Simplifying t = 3.150581317Subproblem 2
t + -1 = -2.150581317 Simplifying t + -1 = -2.150581317 Reorder the terms: -1 + t = -2.150581317 Solving -1 + t = -2.150581317 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 = -2.150581317 + 1 Combine like terms: -1 + 1 = 0 0 + t = -2.150581317 + 1 t = -2.150581317 + 1 Combine like terms: -2.150581317 + 1 = -1.150581317 t = -1.150581317 Simplifying t = -1.150581317Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.150581317, -1.150581317}Solution
t = {3.150581317, -1.150581317}
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