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Simplifying t2 + -25t + 125 = 0 Reorder the terms: 125 + -25t + t2 = 0 Solving 125 + -25t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '-125' to each side of the equation. 125 + -25t + -125 + t2 = 0 + -125 Reorder the terms: 125 + -125 + -25t + t2 = 0 + -125 Combine like terms: 125 + -125 = 0 0 + -25t + t2 = 0 + -125 -25t + t2 = 0 + -125 Combine like terms: 0 + -125 = -125 -25t + t2 = -125 The t term is -25t. Take half its coefficient (-12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. -25t + 156.25 + t2 = -125 + 156.25 Reorder the terms: 156.25 + -25t + t2 = -125 + 156.25 Combine like terms: -125 + 156.25 = 31.25 156.25 + -25t + t2 = 31.25 Factor a perfect square on the left side: (t + -12.5)(t + -12.5) = 31.25 Calculate the square root of the right side: 5.590169944 Break this problem into two subproblems by setting (t + -12.5) equal to 5.590169944 and -5.590169944.Subproblem 1
t + -12.5 = 5.590169944 Simplifying t + -12.5 = 5.590169944 Reorder the terms: -12.5 + t = 5.590169944 Solving -12.5 + t = 5.590169944 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + t = 5.590169944 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + t = 5.590169944 + 12.5 t = 5.590169944 + 12.5 Combine like terms: 5.590169944 + 12.5 = 18.090169944 t = 18.090169944 Simplifying t = 18.090169944Subproblem 2
t + -12.5 = -5.590169944 Simplifying t + -12.5 = -5.590169944 Reorder the terms: -12.5 + t = -5.590169944 Solving -12.5 + t = -5.590169944 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + t = -5.590169944 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + t = -5.590169944 + 12.5 t = -5.590169944 + 12.5 Combine like terms: -5.590169944 + 12.5 = 6.909830056 t = 6.909830056 Simplifying t = 6.909830056Solution
The solution to the problem is based on the solutions from the subproblems. t = {18.090169944, 6.909830056}
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