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Simplifying -16t2 + 200t + 3 = 0 Reorder the terms: 3 + 200t + -16t2 = 0 Solving 3 + 200t + -16t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -0.1875 + -12.5t + t2 = 0 Move the constant term to the right: Add '0.1875' to each side of the equation. -0.1875 + -12.5t + 0.1875 + t2 = 0 + 0.1875 Reorder the terms: -0.1875 + 0.1875 + -12.5t + t2 = 0 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + -12.5t + t2 = 0 + 0.1875 -12.5t + t2 = 0 + 0.1875 Combine like terms: 0 + 0.1875 = 0.1875 -12.5t + t2 = 0.1875 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 = 0.1875 + 39.0625 Reorder the terms: 39.0625 + -12.5t + t2 = 0.1875 + 39.0625 Combine like terms: 0.1875 + 39.0625 = 39.25 39.0625 + -12.5t + t2 = 39.25 Factor a perfect square on the left side: (t + -6.25)(t + -6.25) = 39.25 Calculate the square root of the right side: 6.264982043 Break this problem into two subproblems by setting (t + -6.25) equal to 6.264982043 and -6.264982043.Subproblem 1
t + -6.25 = 6.264982043 Simplifying t + -6.25 = 6.264982043 Reorder the terms: -6.25 + t = 6.264982043 Solving -6.25 + t = 6.264982043 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 = 6.264982043 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + t = 6.264982043 + 6.25 t = 6.264982043 + 6.25 Combine like terms: 6.264982043 + 6.25 = 12.514982043 t = 12.514982043 Simplifying t = 12.514982043Subproblem 2
t + -6.25 = -6.264982043 Simplifying t + -6.25 = -6.264982043 Reorder the terms: -6.25 + t = -6.264982043 Solving -6.25 + t = -6.264982043 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 = -6.264982043 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + t = -6.264982043 + 6.25 t = -6.264982043 + 6.25 Combine like terms: -6.264982043 + 6.25 = -0.014982043 t = -0.014982043 Simplifying t = -0.014982043Solution
The solution to the problem is based on the solutions from the subproblems. t = {12.514982043, -0.014982043}
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