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Simplifying t2 + -10t + -3 = 0 Reorder the terms: -3 + -10t + t2 = 0 Solving -3 + -10t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + -10t + 3 + t2 = 0 + 3 Reorder the terms: -3 + 3 + -10t + t2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -10t + t2 = 0 + 3 -10t + t2 = 0 + 3 Combine like terms: 0 + 3 = 3 -10t + t2 = 3 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 = 3 + 25 Reorder the terms: 25 + -10t + t2 = 3 + 25 Combine like terms: 3 + 25 = 28 25 + -10t + t2 = 28 Factor a perfect square on the left side: (t + -5)(t + -5) = 28 Calculate the square root of the right side: 5.291502622 Break this problem into two subproblems by setting (t + -5) equal to 5.291502622 and -5.291502622.Subproblem 1
t + -5 = 5.291502622 Simplifying t + -5 = 5.291502622 Reorder the terms: -5 + t = 5.291502622 Solving -5 + t = 5.291502622 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 = 5.291502622 + 5 Combine like terms: -5 + 5 = 0 0 + t = 5.291502622 + 5 t = 5.291502622 + 5 Combine like terms: 5.291502622 + 5 = 10.291502622 t = 10.291502622 Simplifying t = 10.291502622Subproblem 2
t + -5 = -5.291502622 Simplifying t + -5 = -5.291502622 Reorder the terms: -5 + t = -5.291502622 Solving -5 + t = -5.291502622 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 = -5.291502622 + 5 Combine like terms: -5 + 5 = 0 0 + t = -5.291502622 + 5 t = -5.291502622 + 5 Combine like terms: -5.291502622 + 5 = -0.291502622 t = -0.291502622 Simplifying t = -0.291502622Solution
The solution to the problem is based on the solutions from the subproblems. t = {10.291502622, -0.291502622}
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