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Simplifying 200t = -16t2 + 150 + 200 Reorder the terms: 200t = 150 + 200 + -16t2 Combine like terms: 150 + 200 = 350 200t = 350 + -16t2 Solving 200t = 350 + -16t2 Solving for variable 't'. Reorder the terms: -350 + 200t + 16t2 = 350 + -16t2 + -350 + 16t2 Reorder the terms: -350 + 200t + 16t2 = 350 + -350 + -16t2 + 16t2 Combine like terms: 350 + -350 = 0 -350 + 200t + 16t2 = 0 + -16t2 + 16t2 -350 + 200t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -350 + 200t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-175 + 100t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-175 + 100t + 8t2)' equal to zero and attempt to solve: Simplifying -175 + 100t + 8t2 = 0 Solving -175 + 100t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -21.875 + 12.5t + t2 = 0 Move the constant term to the right: Add '21.875' to each side of the equation. -21.875 + 12.5t + 21.875 + t2 = 0 + 21.875 Reorder the terms: -21.875 + 21.875 + 12.5t + t2 = 0 + 21.875 Combine like terms: -21.875 + 21.875 = 0.000 0.000 + 12.5t + t2 = 0 + 21.875 12.5t + t2 = 0 + 21.875 Combine like terms: 0 + 21.875 = 21.875 12.5t + t2 = 21.875 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 = 21.875 + 39.0625 Reorder the terms: 39.0625 + 12.5t + t2 = 21.875 + 39.0625 Combine like terms: 21.875 + 39.0625 = 60.9375 39.0625 + 12.5t + t2 = 60.9375 Factor a perfect square on the left side: (t + 6.25)(t + 6.25) = 60.9375 Calculate the square root of the right side: 7.806247498 Break this problem into two subproblems by setting (t + 6.25) equal to 7.806247498 and -7.806247498.Subproblem 1
t + 6.25 = 7.806247498 Simplifying t + 6.25 = 7.806247498 Reorder the terms: 6.25 + t = 7.806247498 Solving 6.25 + t = 7.806247498 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 = 7.806247498 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 0.00 + t = 7.806247498 + -6.25 t = 7.806247498 + -6.25 Combine like terms: 7.806247498 + -6.25 = 1.556247498 t = 1.556247498 Simplifying t = 1.556247498Subproblem 2
t + 6.25 = -7.806247498 Simplifying t + 6.25 = -7.806247498 Reorder the terms: 6.25 + t = -7.806247498 Solving 6.25 + t = -7.806247498 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 = -7.806247498 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 0.00 + t = -7.806247498 + -6.25 t = -7.806247498 + -6.25 Combine like terms: -7.806247498 + -6.25 = -14.056247498 t = -14.056247498 Simplifying t = -14.056247498Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.556247498, -14.056247498}Solution
t = {1.556247498, -14.056247498}
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