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Simplifying 0 = -16t2 + 100t + 200 Reorder the terms: 0 = 200 + 100t + -16t2 Solving 0 = 200 + 100t + -16t2 Solving for variable 't'. Combine like terms: 0 + -200 = -200 -200 + -100t + 16t2 = 200 + 100t + -16t2 + -200 + -100t + 16t2 Reorder the terms: -200 + -100t + 16t2 = 200 + -200 + 100t + -100t + -16t2 + 16t2 Combine like terms: 200 + -200 = 0 -200 + -100t + 16t2 = 0 + 100t + -100t + -16t2 + 16t2 -200 + -100t + 16t2 = 100t + -100t + -16t2 + 16t2 Combine like terms: 100t + -100t = 0 -200 + -100t + 16t2 = 0 + -16t2 + 16t2 -200 + -100t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -200 + -100t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-50 + -25t + 4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-50 + -25t + 4t2)' equal to zero and attempt to solve: Simplifying -50 + -25t + 4t2 = 0 Solving -50 + -25t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -12.5 + -6.25t + t2 = 0 Move the constant term to the right: Add '12.5' to each side of the equation. -12.5 + -6.25t + 12.5 + t2 = 0 + 12.5 Reorder the terms: -12.5 + 12.5 + -6.25t + t2 = 0 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + -6.25t + t2 = 0 + 12.5 -6.25t + t2 = 0 + 12.5 Combine like terms: 0 + 12.5 = 12.5 -6.25t + t2 = 12.5 The t term is -6.25t. Take half its coefficient (-3.125). Square it (9.765625) and add it to both sides. Add '9.765625' to each side of the equation. -6.25t + 9.765625 + t2 = 12.5 + 9.765625 Reorder the terms: 9.765625 + -6.25t + t2 = 12.5 + 9.765625 Combine like terms: 12.5 + 9.765625 = 22.265625 9.765625 + -6.25t + t2 = 22.265625 Factor a perfect square on the left side: (t + -3.125)(t + -3.125) = 22.265625 Calculate the square root of the right side: 4.718646522 Break this problem into two subproblems by setting (t + -3.125) equal to 4.718646522 and -4.718646522.Subproblem 1
t + -3.125 = 4.718646522 Simplifying t + -3.125 = 4.718646522 Reorder the terms: -3.125 + t = 4.718646522 Solving -3.125 + t = 4.718646522 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.125' to each side of the equation. -3.125 + 3.125 + t = 4.718646522 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + t = 4.718646522 + 3.125 t = 4.718646522 + 3.125 Combine like terms: 4.718646522 + 3.125 = 7.843646522 t = 7.843646522 Simplifying t = 7.843646522Subproblem 2
t + -3.125 = -4.718646522 Simplifying t + -3.125 = -4.718646522 Reorder the terms: -3.125 + t = -4.718646522 Solving -3.125 + t = -4.718646522 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.125' to each side of the equation. -3.125 + 3.125 + t = -4.718646522 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + t = -4.718646522 + 3.125 t = -4.718646522 + 3.125 Combine like terms: -4.718646522 + 3.125 = -1.593646522 t = -1.593646522 Simplifying t = -1.593646522Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.843646522, -1.593646522}Solution
t = {7.843646522, -1.593646522}
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