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Simplifying t2 + -17t + 36 = 0 Reorder the terms: 36 + -17t + t2 = 0 Solving 36 + -17t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '-36' to each side of the equation. 36 + -17t + -36 + t2 = 0 + -36 Reorder the terms: 36 + -36 + -17t + t2 = 0 + -36 Combine like terms: 36 + -36 = 0 0 + -17t + t2 = 0 + -36 -17t + t2 = 0 + -36 Combine like terms: 0 + -36 = -36 -17t + t2 = -36 The t term is -17t. Take half its coefficient (-8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. -17t + 72.25 + t2 = -36 + 72.25 Reorder the terms: 72.25 + -17t + t2 = -36 + 72.25 Combine like terms: -36 + 72.25 = 36.25 72.25 + -17t + t2 = 36.25 Factor a perfect square on the left side: (t + -8.5)(t + -8.5) = 36.25 Calculate the square root of the right side: 6.020797289 Break this problem into two subproblems by setting (t + -8.5) equal to 6.020797289 and -6.020797289.Subproblem 1
t + -8.5 = 6.020797289 Simplifying t + -8.5 = 6.020797289 Reorder the terms: -8.5 + t = 6.020797289 Solving -8.5 + t = 6.020797289 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + t = 6.020797289 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + t = 6.020797289 + 8.5 t = 6.020797289 + 8.5 Combine like terms: 6.020797289 + 8.5 = 14.520797289 t = 14.520797289 Simplifying t = 14.520797289Subproblem 2
t + -8.5 = -6.020797289 Simplifying t + -8.5 = -6.020797289 Reorder the terms: -8.5 + t = -6.020797289 Solving -8.5 + t = -6.020797289 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + t = -6.020797289 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + t = -6.020797289 + 8.5 t = -6.020797289 + 8.5 Combine like terms: -6.020797289 + 8.5 = 2.479202711 t = 2.479202711 Simplifying t = 2.479202711Solution
The solution to the problem is based on the solutions from the subproblems. t = {14.520797289, 2.479202711}
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