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Simplifying 4t2 + -40t + 25 = 0 Reorder the terms: 25 + -40t + 4t2 = 0 Solving 25 + -40t + 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'. 6.25 + -10t + t2 = 0 Move the constant term to the right: Add '-6.25' to each side of the equation. 6.25 + -10t + -6.25 + t2 = 0 + -6.25 Reorder the terms: 6.25 + -6.25 + -10t + t2 = 0 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 0.00 + -10t + t2 = 0 + -6.25 -10t + t2 = 0 + -6.25 Combine like terms: 0 + -6.25 = -6.25 -10t + t2 = -6.25 The t term is -10t. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10t + 25 + t2 = -6.25 + 25 Reorder the terms: 25 + -10t + t2 = -6.25 + 25 Combine like terms: -6.25 + 25 = 18.75 25 + -10t + t2 = 18.75 Factor a perfect square on the left side: (t + -5)(t + -5) = 18.75 Calculate the square root of the right side: 4.330127019 Break this problem into two subproblems by setting (t + -5) equal to 4.330127019 and -4.330127019.Subproblem 1
t + -5 = 4.330127019 Simplifying t + -5 = 4.330127019 Reorder the terms: -5 + t = 4.330127019 Solving -5 + t = 4.330127019 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + t = 4.330127019 + 5 Combine like terms: -5 + 5 = 0 0 + t = 4.330127019 + 5 t = 4.330127019 + 5 Combine like terms: 4.330127019 + 5 = 9.330127019 t = 9.330127019 Simplifying t = 9.330127019Subproblem 2
t + -5 = -4.330127019 Simplifying t + -5 = -4.330127019 Reorder the terms: -5 + t = -4.330127019 Solving -5 + t = -4.330127019 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + t = -4.330127019 + 5 Combine like terms: -5 + 5 = 0 0 + t = -4.330127019 + 5 t = -4.330127019 + 5 Combine like terms: -4.330127019 + 5 = 0.669872981 t = 0.669872981 Simplifying t = 0.669872981Solution
The solution to the problem is based on the solutions from the subproblems. t = {9.330127019, 0.669872981}
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