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Simplifying 4t2 + -4t + -253.14 = 0 Reorder the terms: -253.14 + -4t + 4t2 = 0 Solving -253.14 + -4t + 4t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -63.285 + -1t + t2 = 0 Move the constant term to the right: Add '63.285' to each side of the equation. -63.285 + -1t + 63.285 + t2 = 0 + 63.285 Reorder the terms: -63.285 + 63.285 + -1t + t2 = 0 + 63.285 Combine like terms: -63.285 + 63.285 = 0.000 0.000 + -1t + t2 = 0 + 63.285 -1t + t2 = 0 + 63.285 Combine like terms: 0 + 63.285 = 63.285 -1t + t2 = 63.285 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 = 63.285 + 0.25 Reorder the terms: 0.25 + -1t + t2 = 63.285 + 0.25 Combine like terms: 63.285 + 0.25 = 63.535 0.25 + -1t + t2 = 63.535 Factor a perfect square on the left side: (t + -0.5)(t + -0.5) = 63.535 Calculate the square root of the right side: 7.970884518 Break this problem into two subproblems by setting (t + -0.5) equal to 7.970884518 and -7.970884518.Subproblem 1
t + -0.5 = 7.970884518 Simplifying t + -0.5 = 7.970884518 Reorder the terms: -0.5 + t = 7.970884518 Solving -0.5 + t = 7.970884518 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 = 7.970884518 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + t = 7.970884518 + 0.5 t = 7.970884518 + 0.5 Combine like terms: 7.970884518 + 0.5 = 8.470884518 t = 8.470884518 Simplifying t = 8.470884518Subproblem 2
t + -0.5 = -7.970884518 Simplifying t + -0.5 = -7.970884518 Reorder the terms: -0.5 + t = -7.970884518 Solving -0.5 + t = -7.970884518 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 = -7.970884518 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + t = -7.970884518 + 0.5 t = -7.970884518 + 0.5 Combine like terms: -7.970884518 + 0.5 = -7.470884518 t = -7.470884518 Simplifying t = -7.470884518Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.470884518, -7.470884518}
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