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Simplifying t2 + -17t + 6 = 0 Reorder the terms: 6 + -17t + t2 = 0 Solving 6 + -17t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '-6' to each side of the equation. 6 + -17t + -6 + t2 = 0 + -6 Reorder the terms: 6 + -6 + -17t + t2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -17t + t2 = 0 + -6 -17t + t2 = 0 + -6 Combine like terms: 0 + -6 = -6 -17t + t2 = -6 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 = -6 + 72.25 Reorder the terms: 72.25 + -17t + t2 = -6 + 72.25 Combine like terms: -6 + 72.25 = 66.25 72.25 + -17t + t2 = 66.25 Factor a perfect square on the left side: (t + -8.5)(t + -8.5) = 66.25 Calculate the square root of the right side: 8.139410298 Break this problem into two subproblems by setting (t + -8.5) equal to 8.139410298 and -8.139410298.Subproblem 1
t + -8.5 = 8.139410298 Simplifying t + -8.5 = 8.139410298 Reorder the terms: -8.5 + t = 8.139410298 Solving -8.5 + t = 8.139410298 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 = 8.139410298 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + t = 8.139410298 + 8.5 t = 8.139410298 + 8.5 Combine like terms: 8.139410298 + 8.5 = 16.639410298 t = 16.639410298 Simplifying t = 16.639410298Subproblem 2
t + -8.5 = -8.139410298 Simplifying t + -8.5 = -8.139410298 Reorder the terms: -8.5 + t = -8.139410298 Solving -8.5 + t = -8.139410298 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 = -8.139410298 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + t = -8.139410298 + 8.5 t = -8.139410298 + 8.5 Combine like terms: -8.139410298 + 8.5 = 0.360589702 t = 0.360589702 Simplifying t = 0.360589702Solution
The solution to the problem is based on the solutions from the subproblems. t = {16.639410298, 0.360589702}
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