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Simplifying t2 + -10t + 12.5 = 0 Reorder the terms: 12.5 + -10t + t2 = 0 Solving 12.5 + -10t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '-12.5' to each side of the equation. 12.5 + -10t + -12.5 + t2 = 0 + -12.5 Reorder the terms: 12.5 + -12.5 + -10t + t2 = 0 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + -10t + t2 = 0 + -12.5 -10t + t2 = 0 + -12.5 Combine like terms: 0 + -12.5 = -12.5 -10t + t2 = -12.5 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 = -12.5 + 25 Reorder the terms: 25 + -10t + t2 = -12.5 + 25 Combine like terms: -12.5 + 25 = 12.5 25 + -10t + t2 = 12.5 Factor a perfect square on the left side: (t + -5)(t + -5) = 12.5 Calculate the square root of the right side: 3.535533906 Break this problem into two subproblems by setting (t + -5) equal to 3.535533906 and -3.535533906.Subproblem 1
t + -5 = 3.535533906 Simplifying t + -5 = 3.535533906 Reorder the terms: -5 + t = 3.535533906 Solving -5 + t = 3.535533906 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 = 3.535533906 + 5 Combine like terms: -5 + 5 = 0 0 + t = 3.535533906 + 5 t = 3.535533906 + 5 Combine like terms: 3.535533906 + 5 = 8.535533906 t = 8.535533906 Simplifying t = 8.535533906Subproblem 2
t + -5 = -3.535533906 Simplifying t + -5 = -3.535533906 Reorder the terms: -5 + t = -3.535533906 Solving -5 + t = -3.535533906 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 = -3.535533906 + 5 Combine like terms: -5 + 5 = 0 0 + t = -3.535533906 + 5 t = -3.535533906 + 5 Combine like terms: -3.535533906 + 5 = 1.464466094 t = 1.464466094 Simplifying t = 1.464466094Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.535533906, 1.464466094}
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