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Simplifying x2 + -17x + 43 = 0 Reorder the terms: 43 + -17x + x2 = 0 Solving 43 + -17x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-43' to each side of the equation. 43 + -17x + -43 + x2 = 0 + -43 Reorder the terms: 43 + -43 + -17x + x2 = 0 + -43 Combine like terms: 43 + -43 = 0 0 + -17x + x2 = 0 + -43 -17x + x2 = 0 + -43 Combine like terms: 0 + -43 = -43 -17x + x2 = -43 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 = -43 + 72.25 Reorder the terms: 72.25 + -17x + x2 = -43 + 72.25 Combine like terms: -43 + 72.25 = 29.25 72.25 + -17x + x2 = 29.25 Factor a perfect square on the left side: (x + -8.5)(x + -8.5) = 29.25 Calculate the square root of the right side: 5.408326913 Break this problem into two subproblems by setting (x + -8.5) equal to 5.408326913 and -5.408326913.Subproblem 1
x + -8.5 = 5.408326913 Simplifying x + -8.5 = 5.408326913 Reorder the terms: -8.5 + x = 5.408326913 Solving -8.5 + x = 5.408326913 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 = 5.408326913 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = 5.408326913 + 8.5 x = 5.408326913 + 8.5 Combine like terms: 5.408326913 + 8.5 = 13.908326913 x = 13.908326913 Simplifying x = 13.908326913Subproblem 2
x + -8.5 = -5.408326913 Simplifying x + -8.5 = -5.408326913 Reorder the terms: -8.5 + x = -5.408326913 Solving -8.5 + x = -5.408326913 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 = -5.408326913 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = -5.408326913 + 8.5 x = -5.408326913 + 8.5 Combine like terms: -5.408326913 + 8.5 = 3.091673087 x = 3.091673087 Simplifying x = 3.091673087Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.908326913, 3.091673087}
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