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Simplifying t2 + -25t + 155 = 0 Reorder the terms: 155 + -25t + t2 = 0 Solving 155 + -25t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '-155' to each side of the equation. 155 + -25t + -155 + t2 = 0 + -155 Reorder the terms: 155 + -155 + -25t + t2 = 0 + -155 Combine like terms: 155 + -155 = 0 0 + -25t + t2 = 0 + -155 -25t + t2 = 0 + -155 Combine like terms: 0 + -155 = -155 -25t + t2 = -155 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 = -155 + 156.25 Reorder the terms: 156.25 + -25t + t2 = -155 + 156.25 Combine like terms: -155 + 156.25 = 1.25 156.25 + -25t + t2 = 1.25 Factor a perfect square on the left side: (t + -12.5)(t + -12.5) = 1.25 Calculate the square root of the right side: 1.118033989 Break this problem into two subproblems by setting (t + -12.5) equal to 1.118033989 and -1.118033989.Subproblem 1
t + -12.5 = 1.118033989 Simplifying t + -12.5 = 1.118033989 Reorder the terms: -12.5 + t = 1.118033989 Solving -12.5 + t = 1.118033989 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 = 1.118033989 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + t = 1.118033989 + 12.5 t = 1.118033989 + 12.5 Combine like terms: 1.118033989 + 12.5 = 13.618033989 t = 13.618033989 Simplifying t = 13.618033989Subproblem 2
t + -12.5 = -1.118033989 Simplifying t + -12.5 = -1.118033989 Reorder the terms: -12.5 + t = -1.118033989 Solving -12.5 + t = -1.118033989 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 = -1.118033989 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + t = -1.118033989 + 12.5 t = -1.118033989 + 12.5 Combine like terms: -1.118033989 + 12.5 = 11.381966011 t = 11.381966011 Simplifying t = 11.381966011Solution
The solution to the problem is based on the solutions from the subproblems. t = {13.618033989, 11.381966011}
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