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Simplifying 200 = -16t2 + 200t Reorder the terms: 200 = 200t + -16t2 Solving 200 = 200t + -16t2 Solving for variable 't'. Reorder the terms: 200 + -200t + 16t2 = 200t + -200t + -16t2 + 16t2 Combine like terms: 200t + -200t = 0 200 + -200t + 16t2 = 0 + -16t2 + 16t2 200 + -200t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 200 + -200t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(25 + -25t + 2t2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(25 + -25t + 2t2)' equal to zero and attempt to solve: Simplifying 25 + -25t + 2t2 = 0 Solving 25 + -25t + 2t2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 12.5 + -12.5t + t2 = 0 Move the constant term to the right: Add '-12.5' to each side of the equation. 12.5 + -12.5t + -12.5 + t2 = 0 + -12.5 Reorder the terms: 12.5 + -12.5 + -12.5t + t2 = 0 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + -12.5t + t2 = 0 + -12.5 -12.5t + t2 = 0 + -12.5 Combine like terms: 0 + -12.5 = -12.5 -12.5t + t2 = -12.5 The t term is -12.5t. Take half its coefficient (-6.25). Square it (39.0625) and add it to both sides. Add '39.0625' to each side of the equation. -12.5t + 39.0625 + t2 = -12.5 + 39.0625 Reorder the terms: 39.0625 + -12.5t + t2 = -12.5 + 39.0625 Combine like terms: -12.5 + 39.0625 = 26.5625 39.0625 + -12.5t + t2 = 26.5625 Factor a perfect square on the left side: (t + -6.25)(t + -6.25) = 26.5625 Calculate the square root of the right side: 5.153882032 Break this problem into two subproblems by setting (t + -6.25) equal to 5.153882032 and -5.153882032.Subproblem 1
t + -6.25 = 5.153882032 Simplifying t + -6.25 = 5.153882032 Reorder the terms: -6.25 + t = 5.153882032 Solving -6.25 + t = 5.153882032 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + t = 5.153882032 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + t = 5.153882032 + 6.25 t = 5.153882032 + 6.25 Combine like terms: 5.153882032 + 6.25 = 11.403882032 t = 11.403882032 Simplifying t = 11.403882032Subproblem 2
t + -6.25 = -5.153882032 Simplifying t + -6.25 = -5.153882032 Reorder the terms: -6.25 + t = -5.153882032 Solving -6.25 + t = -5.153882032 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + t = -5.153882032 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + t = -5.153882032 + 6.25 t = -5.153882032 + 6.25 Combine like terms: -5.153882032 + 6.25 = 1.096117968 t = 1.096117968 Simplifying t = 1.096117968Solution
The solution to the problem is based on the solutions from the subproblems. t = {11.403882032, 1.096117968}Solution
t = {11.403882032, 1.096117968}
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