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Simplifying -9 + -10t + t2 = 0 Solving -9 + -10t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + -10t + 9 + t2 = 0 + 9 Reorder the terms: -9 + 9 + -10t + t2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -10t + t2 = 0 + 9 -10t + t2 = 0 + 9 Combine like terms: 0 + 9 = 9 -10t + t2 = 9 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 = 9 + 25 Reorder the terms: 25 + -10t + t2 = 9 + 25 Combine like terms: 9 + 25 = 34 25 + -10t + t2 = 34 Factor a perfect square on the left side: (t + -5)(t + -5) = 34 Calculate the square root of the right side: 5.830951895 Break this problem into two subproblems by setting (t + -5) equal to 5.830951895 and -5.830951895.Subproblem 1
t + -5 = 5.830951895 Simplifying t + -5 = 5.830951895 Reorder the terms: -5 + t = 5.830951895 Solving -5 + t = 5.830951895 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 = 5.830951895 + 5 Combine like terms: -5 + 5 = 0 0 + t = 5.830951895 + 5 t = 5.830951895 + 5 Combine like terms: 5.830951895 + 5 = 10.830951895 t = 10.830951895 Simplifying t = 10.830951895Subproblem 2
t + -5 = -5.830951895 Simplifying t + -5 = -5.830951895 Reorder the terms: -5 + t = -5.830951895 Solving -5 + t = -5.830951895 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 = -5.830951895 + 5 Combine like terms: -5 + 5 = 0 0 + t = -5.830951895 + 5 t = -5.830951895 + 5 Combine like terms: -5.830951895 + 5 = -0.830951895 t = -0.830951895 Simplifying t = -0.830951895Solution
The solution to the problem is based on the solutions from the subproblems. t = {10.830951895, -0.830951895}
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