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Simplifying 0 = -16t2 + 64t + 200 Reorder the terms: 0 = 200 + 64t + -16t2 Solving 0 = 200 + 64t + -16t2 Solving for variable 't'. Combine like terms: 0 + -200 = -200 -200 + -64t + 16t2 = 200 + 64t + -16t2 + -200 + -64t + 16t2 Reorder the terms: -200 + -64t + 16t2 = 200 + -200 + 64t + -64t + -16t2 + 16t2 Combine like terms: 200 + -200 = 0 -200 + -64t + 16t2 = 0 + 64t + -64t + -16t2 + 16t2 -200 + -64t + 16t2 = 64t + -64t + -16t2 + 16t2 Combine like terms: 64t + -64t = 0 -200 + -64t + 16t2 = 0 + -16t2 + 16t2 -200 + -64t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -200 + -64t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(-25 + -8t + 2t2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(-25 + -8t + 2t2)' equal to zero and attempt to solve: Simplifying -25 + -8t + 2t2 = 0 Solving -25 + -8t + 2t2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -12.5 + -4t + t2 = 0 Move the constant term to the right: Add '12.5' to each side of the equation. -12.5 + -4t + 12.5 + t2 = 0 + 12.5 Reorder the terms: -12.5 + 12.5 + -4t + t2 = 0 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + -4t + t2 = 0 + 12.5 -4t + t2 = 0 + 12.5 Combine like terms: 0 + 12.5 = 12.5 -4t + t2 = 12.5 The t term is -4t. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4t + 4 + t2 = 12.5 + 4 Reorder the terms: 4 + -4t + t2 = 12.5 + 4 Combine like terms: 12.5 + 4 = 16.5 4 + -4t + t2 = 16.5 Factor a perfect square on the left side: (t + -2)(t + -2) = 16.5 Calculate the square root of the right side: 4.062019202 Break this problem into two subproblems by setting (t + -2) equal to 4.062019202 and -4.062019202.Subproblem 1
t + -2 = 4.062019202 Simplifying t + -2 = 4.062019202 Reorder the terms: -2 + t = 4.062019202 Solving -2 + t = 4.062019202 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + t = 4.062019202 + 2 Combine like terms: -2 + 2 = 0 0 + t = 4.062019202 + 2 t = 4.062019202 + 2 Combine like terms: 4.062019202 + 2 = 6.062019202 t = 6.062019202 Simplifying t = 6.062019202Subproblem 2
t + -2 = -4.062019202 Simplifying t + -2 = -4.062019202 Reorder the terms: -2 + t = -4.062019202 Solving -2 + t = -4.062019202 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + t = -4.062019202 + 2 Combine like terms: -2 + 2 = 0 0 + t = -4.062019202 + 2 t = -4.062019202 + 2 Combine like terms: -4.062019202 + 2 = -2.062019202 t = -2.062019202 Simplifying t = -2.062019202Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.062019202, -2.062019202}Solution
t = {6.062019202, -2.062019202}
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