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Simplifying t2 + -1t = 40 + 4t Reorder the terms: -1t + t2 = 40 + 4t Solving -1t + t2 = 40 + 4t Solving for variable 't'. Reorder the terms: -40 + -1t + -4t + t2 = 40 + 4t + -40 + -4t Combine like terms: -1t + -4t = -5t -40 + -5t + t2 = 40 + 4t + -40 + -4t Reorder the terms: -40 + -5t + t2 = 40 + -40 + 4t + -4t Combine like terms: 40 + -40 = 0 -40 + -5t + t2 = 0 + 4t + -4t -40 + -5t + t2 = 4t + -4t Combine like terms: 4t + -4t = 0 -40 + -5t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '40' to each side of the equation. -40 + -5t + 40 + t2 = 0 + 40 Reorder the terms: -40 + 40 + -5t + t2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + -5t + t2 = 0 + 40 -5t + t2 = 0 + 40 Combine like terms: 0 + 40 = 40 -5t + t2 = 40 The t term is -5t. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5t + 6.25 + t2 = 40 + 6.25 Reorder the terms: 6.25 + -5t + t2 = 40 + 6.25 Combine like terms: 40 + 6.25 = 46.25 6.25 + -5t + t2 = 46.25 Factor a perfect square on the left side: (t + -2.5)(t + -2.5) = 46.25 Calculate the square root of the right side: 6.800735254 Break this problem into two subproblems by setting (t + -2.5) equal to 6.800735254 and -6.800735254.Subproblem 1
t + -2.5 = 6.800735254 Simplifying t + -2.5 = 6.800735254 Reorder the terms: -2.5 + t = 6.800735254 Solving -2.5 + t = 6.800735254 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + t = 6.800735254 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + t = 6.800735254 + 2.5 t = 6.800735254 + 2.5 Combine like terms: 6.800735254 + 2.5 = 9.300735254 t = 9.300735254 Simplifying t = 9.300735254Subproblem 2
t + -2.5 = -6.800735254 Simplifying t + -2.5 = -6.800735254 Reorder the terms: -2.5 + t = -6.800735254 Solving -2.5 + t = -6.800735254 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + t = -6.800735254 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + t = -6.800735254 + 2.5 t = -6.800735254 + 2.5 Combine like terms: -6.800735254 + 2.5 = -4.300735254 t = -4.300735254 Simplifying t = -4.300735254Solution
The solution to the problem is based on the solutions from the subproblems. t = {9.300735254, -4.300735254}
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