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Simplifying 0 = -16t2 + 16t + 200 Reorder the terms: 0 = 200 + 16t + -16t2 Solving 0 = 200 + 16t + -16t2 Solving for variable 't'. Combine like terms: 0 + -200 = -200 -200 + -16t + 16t2 = 200 + 16t + -16t2 + -200 + -16t + 16t2 Reorder the terms: -200 + -16t + 16t2 = 200 + -200 + 16t + -16t + -16t2 + 16t2 Combine like terms: 200 + -200 = 0 -200 + -16t + 16t2 = 0 + 16t + -16t + -16t2 + 16t2 -200 + -16t + 16t2 = 16t + -16t + -16t2 + 16t2 Combine like terms: 16t + -16t = 0 -200 + -16t + 16t2 = 0 + -16t2 + 16t2 -200 + -16t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -200 + -16t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(-25 + -2t + 2t2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(-25 + -2t + 2t2)' equal to zero and attempt to solve: Simplifying -25 + -2t + 2t2 = 0 Solving -25 + -2t + 2t2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -12.5 + -1t + t2 = 0 Move the constant term to the right: Add '12.5' to each side of the equation. -12.5 + -1t + 12.5 + t2 = 0 + 12.5 Reorder the terms: -12.5 + 12.5 + -1t + t2 = 0 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + -1t + t2 = 0 + 12.5 -1t + t2 = 0 + 12.5 Combine like terms: 0 + 12.5 = 12.5 -1t + t2 = 12.5 The t term is -1t. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1t + 0.25 + t2 = 12.5 + 0.25 Reorder the terms: 0.25 + -1t + t2 = 12.5 + 0.25 Combine like terms: 12.5 + 0.25 = 12.75 0.25 + -1t + t2 = 12.75 Factor a perfect square on the left side: (t + -0.5)(t + -0.5) = 12.75 Calculate the square root of the right side: 3.570714214 Break this problem into two subproblems by setting (t + -0.5) equal to 3.570714214 and -3.570714214.Subproblem 1
t + -0.5 = 3.570714214 Simplifying t + -0.5 = 3.570714214 Reorder the terms: -0.5 + t = 3.570714214 Solving -0.5 + t = 3.570714214 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + t = 3.570714214 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + t = 3.570714214 + 0.5 t = 3.570714214 + 0.5 Combine like terms: 3.570714214 + 0.5 = 4.070714214 t = 4.070714214 Simplifying t = 4.070714214Subproblem 2
t + -0.5 = -3.570714214 Simplifying t + -0.5 = -3.570714214 Reorder the terms: -0.5 + t = -3.570714214 Solving -0.5 + t = -3.570714214 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + t = -3.570714214 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + t = -3.570714214 + 0.5 t = -3.570714214 + 0.5 Combine like terms: -3.570714214 + 0.5 = -3.070714214 t = -3.070714214 Simplifying t = -3.070714214Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.070714214, -3.070714214}Solution
t = {4.070714214, -3.070714214}
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