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Simplifying t2 + -10t + 25 = 176 Reorder the terms: 25 + -10t + t2 = 176 Solving 25 + -10t + t2 = 176 Solving for variable 't'. Reorder the terms: 25 + -176 + -10t + t2 = 176 + -176 Combine like terms: 25 + -176 = -151 -151 + -10t + t2 = 176 + -176 Combine like terms: 176 + -176 = 0 -151 + -10t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '151' to each side of the equation. -151 + -10t + 151 + t2 = 0 + 151 Reorder the terms: -151 + 151 + -10t + t2 = 0 + 151 Combine like terms: -151 + 151 = 0 0 + -10t + t2 = 0 + 151 -10t + t2 = 0 + 151 Combine like terms: 0 + 151 = 151 -10t + t2 = 151 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 = 151 + 25 Reorder the terms: 25 + -10t + t2 = 151 + 25 Combine like terms: 151 + 25 = 176 25 + -10t + t2 = 176 Factor a perfect square on the left side: (t + -5)(t + -5) = 176 Calculate the square root of the right side: 13.266499161 Break this problem into two subproblems by setting (t + -5) equal to 13.266499161 and -13.266499161.Subproblem 1
t + -5 = 13.266499161 Simplifying t + -5 = 13.266499161 Reorder the terms: -5 + t = 13.266499161 Solving -5 + t = 13.266499161 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 = 13.266499161 + 5 Combine like terms: -5 + 5 = 0 0 + t = 13.266499161 + 5 t = 13.266499161 + 5 Combine like terms: 13.266499161 + 5 = 18.266499161 t = 18.266499161 Simplifying t = 18.266499161Subproblem 2
t + -5 = -13.266499161 Simplifying t + -5 = -13.266499161 Reorder the terms: -5 + t = -13.266499161 Solving -5 + t = -13.266499161 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 = -13.266499161 + 5 Combine like terms: -5 + 5 = 0 0 + t = -13.266499161 + 5 t = -13.266499161 + 5 Combine like terms: -13.266499161 + 5 = -8.266499161 t = -8.266499161 Simplifying t = -8.266499161Solution
The solution to the problem is based on the solutions from the subproblems. t = {18.266499161, -8.266499161}
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