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Simplifying 0 = -16t2 + 32t + 252 Reorder the terms: 0 = 252 + 32t + -16t2 Solving 0 = 252 + 32t + -16t2 Solving for variable 't'. Combine like terms: 0 + -252 = -252 -252 + -32t + 16t2 = 252 + 32t + -16t2 + -252 + -32t + 16t2 Reorder the terms: -252 + -32t + 16t2 = 252 + -252 + 32t + -32t + -16t2 + 16t2 Combine like terms: 252 + -252 = 0 -252 + -32t + 16t2 = 0 + 32t + -32t + -16t2 + 16t2 -252 + -32t + 16t2 = 32t + -32t + -16t2 + 16t2 Combine like terms: 32t + -32t = 0 -252 + -32t + 16t2 = 0 + -16t2 + 16t2 -252 + -32t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -252 + -32t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-63 + -8t + 4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-63 + -8t + 4t2)' equal to zero and attempt to solve: Simplifying -63 + -8t + 4t2 = 0 Solving -63 + -8t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -15.75 + -2t + t2 = 0 Move the constant term to the right: Add '15.75' to each side of the equation. -15.75 + -2t + 15.75 + t2 = 0 + 15.75 Reorder the terms: -15.75 + 15.75 + -2t + t2 = 0 + 15.75 Combine like terms: -15.75 + 15.75 = 0.00 0.00 + -2t + t2 = 0 + 15.75 -2t + t2 = 0 + 15.75 Combine like terms: 0 + 15.75 = 15.75 -2t + t2 = 15.75 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 = 15.75 + 1 Reorder the terms: 1 + -2t + t2 = 15.75 + 1 Combine like terms: 15.75 + 1 = 16.75 1 + -2t + t2 = 16.75 Factor a perfect square on the left side: (t + -1)(t + -1) = 16.75 Calculate the square root of the right side: 4.092676386 Break this problem into two subproblems by setting (t + -1) equal to 4.092676386 and -4.092676386.Subproblem 1
t + -1 = 4.092676386 Simplifying t + -1 = 4.092676386 Reorder the terms: -1 + t = 4.092676386 Solving -1 + t = 4.092676386 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 = 4.092676386 + 1 Combine like terms: -1 + 1 = 0 0 + t = 4.092676386 + 1 t = 4.092676386 + 1 Combine like terms: 4.092676386 + 1 = 5.092676386 t = 5.092676386 Simplifying t = 5.092676386Subproblem 2
t + -1 = -4.092676386 Simplifying t + -1 = -4.092676386 Reorder the terms: -1 + t = -4.092676386 Solving -1 + t = -4.092676386 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 = -4.092676386 + 1 Combine like terms: -1 + 1 = 0 0 + t = -4.092676386 + 1 t = -4.092676386 + 1 Combine like terms: -4.092676386 + 1 = -3.092676386 t = -3.092676386 Simplifying t = -3.092676386Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.092676386, -3.092676386}Solution
t = {5.092676386, -3.092676386}
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