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Simplifying 0 = -16t2 + 32t + 200 Reorder the terms: 0 = 200 + 32t + -16t2 Solving 0 = 200 + 32t + -16t2 Solving for variable 't'. Combine like terms: 0 + -200 = -200 -200 + -32t + 16t2 = 200 + 32t + -16t2 + -200 + -32t + 16t2 Reorder the terms: -200 + -32t + 16t2 = 200 + -200 + 32t + -32t + -16t2 + 16t2 Combine like terms: 200 + -200 = 0 -200 + -32t + 16t2 = 0 + 32t + -32t + -16t2 + 16t2 -200 + -32t + 16t2 = 32t + -32t + -16t2 + 16t2 Combine like terms: 32t + -32t = 0 -200 + -32t + 16t2 = 0 + -16t2 + 16t2 -200 + -32t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -200 + -32t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(-25 + -4t + 2t2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(-25 + -4t + 2t2)' equal to zero and attempt to solve: Simplifying -25 + -4t + 2t2 = 0 Solving -25 + -4t + 2t2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -12.5 + -2t + t2 = 0 Move the constant term to the right: Add '12.5' to each side of the equation. -12.5 + -2t + 12.5 + t2 = 0 + 12.5 Reorder the terms: -12.5 + 12.5 + -2t + t2 = 0 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + -2t + t2 = 0 + 12.5 -2t + t2 = 0 + 12.5 Combine like terms: 0 + 12.5 = 12.5 -2t + t2 = 12.5 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 = 12.5 + 1 Reorder the terms: 1 + -2t + t2 = 12.5 + 1 Combine like terms: 12.5 + 1 = 13.5 1 + -2t + t2 = 13.5 Factor a perfect square on the left side: (t + -1)(t + -1) = 13.5 Calculate the square root of the right side: 3.674234614 Break this problem into two subproblems by setting (t + -1) equal to 3.674234614 and -3.674234614.Subproblem 1
t + -1 = 3.674234614 Simplifying t + -1 = 3.674234614 Reorder the terms: -1 + t = 3.674234614 Solving -1 + t = 3.674234614 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 = 3.674234614 + 1 Combine like terms: -1 + 1 = 0 0 + t = 3.674234614 + 1 t = 3.674234614 + 1 Combine like terms: 3.674234614 + 1 = 4.674234614 t = 4.674234614 Simplifying t = 4.674234614Subproblem 2
t + -1 = -3.674234614 Simplifying t + -1 = -3.674234614 Reorder the terms: -1 + t = -3.674234614 Solving -1 + t = -3.674234614 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 = -3.674234614 + 1 Combine like terms: -1 + 1 = 0 0 + t = -3.674234614 + 1 t = -3.674234614 + 1 Combine like terms: -3.674234614 + 1 = -2.674234614 t = -2.674234614 Simplifying t = -2.674234614Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.674234614, -2.674234614}Solution
t = {4.674234614, -2.674234614}
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