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Simplifying -16t2 + 128t + 200 = 0 Reorder the terms: 200 + 128t + -16t2 = 0 Solving 200 + 128t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '8'. 8(25 + 16t + -2t2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(25 + 16t + -2t2)' equal to zero and attempt to solve: Simplifying 25 + 16t + -2t2 = 0 Solving 25 + 16t + -2t2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -12.5 + -8t + t2 = 0 Move the constant term to the right: Add '12.5' to each side of the equation. -12.5 + -8t + 12.5 + t2 = 0 + 12.5 Reorder the terms: -12.5 + 12.5 + -8t + t2 = 0 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + -8t + t2 = 0 + 12.5 -8t + t2 = 0 + 12.5 Combine like terms: 0 + 12.5 = 12.5 -8t + t2 = 12.5 The t term is -8t. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8t + 16 + t2 = 12.5 + 16 Reorder the terms: 16 + -8t + t2 = 12.5 + 16 Combine like terms: 12.5 + 16 = 28.5 16 + -8t + t2 = 28.5 Factor a perfect square on the left side: (t + -4)(t + -4) = 28.5 Calculate the square root of the right side: 5.338539126 Break this problem into two subproblems by setting (t + -4) equal to 5.338539126 and -5.338539126.Subproblem 1
t + -4 = 5.338539126 Simplifying t + -4 = 5.338539126 Reorder the terms: -4 + t = 5.338539126 Solving -4 + t = 5.338539126 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + t = 5.338539126 + 4 Combine like terms: -4 + 4 = 0 0 + t = 5.338539126 + 4 t = 5.338539126 + 4 Combine like terms: 5.338539126 + 4 = 9.338539126 t = 9.338539126 Simplifying t = 9.338539126Subproblem 2
t + -4 = -5.338539126 Simplifying t + -4 = -5.338539126 Reorder the terms: -4 + t = -5.338539126 Solving -4 + t = -5.338539126 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + t = -5.338539126 + 4 Combine like terms: -4 + 4 = 0 0 + t = -5.338539126 + 4 t = -5.338539126 + 4 Combine like terms: -5.338539126 + 4 = -1.338539126 t = -1.338539126 Simplifying t = -1.338539126Solution
The solution to the problem is based on the solutions from the subproblems. t = {9.338539126, -1.338539126}Solution
t = {9.338539126, -1.338539126}
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