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Simplifying 0 = 4t2 + -13t + -10 Reorder the terms: 0 = -10 + -13t + 4t2 Solving 0 = -10 + -13t + 4t2 Solving for variable 't'. Combine like terms: 0 + 10 = 10 10 + 13t + -4t2 = -10 + -13t + 4t2 + 10 + 13t + -4t2 Reorder the terms: 10 + 13t + -4t2 = -10 + 10 + -13t + 13t + 4t2 + -4t2 Combine like terms: -10 + 10 = 0 10 + 13t + -4t2 = 0 + -13t + 13t + 4t2 + -4t2 10 + 13t + -4t2 = -13t + 13t + 4t2 + -4t2 Combine like terms: -13t + 13t = 0 10 + 13t + -4t2 = 0 + 4t2 + -4t2 10 + 13t + -4t2 = 4t2 + -4t2 Combine like terms: 4t2 + -4t2 = 0 10 + 13t + -4t2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -2.5 + -3.25t + t2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + -3.25t + 2.5 + t2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + -3.25t + t2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + -3.25t + t2 = 0 + 2.5 -3.25t + t2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 -3.25t + t2 = 2.5 The t term is -3.25t. Take half its coefficient (-1.625). Square it (2.640625) and add it to both sides. Add '2.640625' to each side of the equation. -3.25t + 2.640625 + t2 = 2.5 + 2.640625 Reorder the terms: 2.640625 + -3.25t + t2 = 2.5 + 2.640625 Combine like terms: 2.5 + 2.640625 = 5.140625 2.640625 + -3.25t + t2 = 5.140625 Factor a perfect square on the left side: (t + -1.625)(t + -1.625) = 5.140625 Calculate the square root of the right side: 2.267294643 Break this problem into two subproblems by setting (t + -1.625) equal to 2.267294643 and -2.267294643.Subproblem 1
t + -1.625 = 2.267294643 Simplifying t + -1.625 = 2.267294643 Reorder the terms: -1.625 + t = 2.267294643 Solving -1.625 + t = 2.267294643 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.625' to each side of the equation. -1.625 + 1.625 + t = 2.267294643 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + t = 2.267294643 + 1.625 t = 2.267294643 + 1.625 Combine like terms: 2.267294643 + 1.625 = 3.892294643 t = 3.892294643 Simplifying t = 3.892294643Subproblem 2
t + -1.625 = -2.267294643 Simplifying t + -1.625 = -2.267294643 Reorder the terms: -1.625 + t = -2.267294643 Solving -1.625 + t = -2.267294643 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.625' to each side of the equation. -1.625 + 1.625 + t = -2.267294643 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + t = -2.267294643 + 1.625 t = -2.267294643 + 1.625 Combine like terms: -2.267294643 + 1.625 = -0.642294643 t = -0.642294643 Simplifying t = -0.642294643Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.892294643, -0.642294643}
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