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Simplifying t2 + -13t + 5 = 0 Reorder the terms: 5 + -13t + t2 = 0 Solving 5 + -13t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + -13t + -5 + t2 = 0 + -5 Reorder the terms: 5 + -5 + -13t + t2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -13t + t2 = 0 + -5 -13t + t2 = 0 + -5 Combine like terms: 0 + -5 = -5 -13t + t2 = -5 The t term is -13t. Take half its coefficient (-6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. -13t + 42.25 + t2 = -5 + 42.25 Reorder the terms: 42.25 + -13t + t2 = -5 + 42.25 Combine like terms: -5 + 42.25 = 37.25 42.25 + -13t + t2 = 37.25 Factor a perfect square on the left side: (t + -6.5)(t + -6.5) = 37.25 Calculate the square root of the right side: 6.103277808 Break this problem into two subproblems by setting (t + -6.5) equal to 6.103277808 and -6.103277808.Subproblem 1
t + -6.5 = 6.103277808 Simplifying t + -6.5 = 6.103277808 Reorder the terms: -6.5 + t = 6.103277808 Solving -6.5 + t = 6.103277808 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + t = 6.103277808 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + t = 6.103277808 + 6.5 t = 6.103277808 + 6.5 Combine like terms: 6.103277808 + 6.5 = 12.603277808 t = 12.603277808 Simplifying t = 12.603277808Subproblem 2
t + -6.5 = -6.103277808 Simplifying t + -6.5 = -6.103277808 Reorder the terms: -6.5 + t = -6.103277808 Solving -6.5 + t = -6.103277808 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + t = -6.103277808 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + t = -6.103277808 + 6.5 t = -6.103277808 + 6.5 Combine like terms: -6.103277808 + 6.5 = 0.396722192 t = 0.396722192 Simplifying t = 0.396722192Solution
The solution to the problem is based on the solutions from the subproblems. t = {12.603277808, 0.396722192}
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