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Simplifying 200 = 4t + t2 Solving 200 = 4t + t2 Solving for variable 't'. Reorder the terms: 200 + -4t + -1t2 = 4t + -4t + t2 + -1t2 Combine like terms: 4t + -4t = 0 200 + -4t + -1t2 = 0 + t2 + -1t2 200 + -4t + -1t2 = t2 + -1t2 Combine like terms: t2 + -1t2 = 0 200 + -4t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -200 + 4t + t2 = 0 Move the constant term to the right: Add '200' to each side of the equation. -200 + 4t + 200 + t2 = 0 + 200 Reorder the terms: -200 + 200 + 4t + t2 = 0 + 200 Combine like terms: -200 + 200 = 0 0 + 4t + t2 = 0 + 200 4t + t2 = 0 + 200 Combine like terms: 0 + 200 = 200 4t + t2 = 200 The t term is 4t. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4t + 4 + t2 = 200 + 4 Reorder the terms: 4 + 4t + t2 = 200 + 4 Combine like terms: 200 + 4 = 204 4 + 4t + t2 = 204 Factor a perfect square on the left side: (t + 2)(t + 2) = 204 Calculate the square root of the right side: 14.282856857 Break this problem into two subproblems by setting (t + 2) equal to 14.282856857 and -14.282856857.Subproblem 1
t + 2 = 14.282856857 Simplifying t + 2 = 14.282856857 Reorder the terms: 2 + t = 14.282856857 Solving 2 + t = 14.282856857 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + t = 14.282856857 + -2 Combine like terms: 2 + -2 = 0 0 + t = 14.282856857 + -2 t = 14.282856857 + -2 Combine like terms: 14.282856857 + -2 = 12.282856857 t = 12.282856857 Simplifying t = 12.282856857Subproblem 2
t + 2 = -14.282856857 Simplifying t + 2 = -14.282856857 Reorder the terms: 2 + t = -14.282856857 Solving 2 + t = -14.282856857 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + t = -14.282856857 + -2 Combine like terms: 2 + -2 = 0 0 + t = -14.282856857 + -2 t = -14.282856857 + -2 Combine like terms: -14.282856857 + -2 = -16.282856857 t = -16.282856857 Simplifying t = -16.282856857Solution
The solution to the problem is based on the solutions from the subproblems. t = {12.282856857, -16.282856857}
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