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Simplifying x2 + -17x + 6 = 0 Reorder the terms: 6 + -17x + x2 = 0 Solving 6 + -17x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-6' to each side of the equation. 6 + -17x + -6 + x2 = 0 + -6 Reorder the terms: 6 + -6 + -17x + x2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -17x + x2 = 0 + -6 -17x + x2 = 0 + -6 Combine like terms: 0 + -6 = -6 -17x + x2 = -6 The x term is -17x. 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. -17x + 72.25 + x2 = -6 + 72.25 Reorder the terms: 72.25 + -17x + x2 = -6 + 72.25 Combine like terms: -6 + 72.25 = 66.25 72.25 + -17x + x2 = 66.25 Factor a perfect square on the left side: (x + -8.5)(x + -8.5) = 66.25 Calculate the square root of the right side: 8.139410298 Break this problem into two subproblems by setting (x + -8.5) equal to 8.139410298 and -8.139410298.Subproblem 1
x + -8.5 = 8.139410298 Simplifying x + -8.5 = 8.139410298 Reorder the terms: -8.5 + x = 8.139410298 Solving -8.5 + x = 8.139410298 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + x = 8.139410298 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = 8.139410298 + 8.5 x = 8.139410298 + 8.5 Combine like terms: 8.139410298 + 8.5 = 16.639410298 x = 16.639410298 Simplifying x = 16.639410298Subproblem 2
x + -8.5 = -8.139410298 Simplifying x + -8.5 = -8.139410298 Reorder the terms: -8.5 + x = -8.139410298 Solving -8.5 + x = -8.139410298 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + x = -8.139410298 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = -8.139410298 + 8.5 x = -8.139410298 + 8.5 Combine like terms: -8.139410298 + 8.5 = 0.360589702 x = 0.360589702 Simplifying x = 0.360589702Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.639410298, 0.360589702}
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