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Simplifying X2 + -17X + 5 = 0 Reorder the terms: 5 + -17X + X2 = 0 Solving 5 + -17X + X2 = 0 Solving for variable 'X'. Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + -17X + -5 + X2 = 0 + -5 Reorder the terms: 5 + -5 + -17X + X2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -17X + X2 = 0 + -5 -17X + X2 = 0 + -5 Combine like terms: 0 + -5 = -5 -17X + X2 = -5 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 = -5 + 72.25 Reorder the terms: 72.25 + -17X + X2 = -5 + 72.25 Combine like terms: -5 + 72.25 = 67.25 72.25 + -17X + X2 = 67.25 Factor a perfect square on the left side: (X + -8.5)(X + -8.5) = 67.25 Calculate the square root of the right side: 8.200609733 Break this problem into two subproblems by setting (X + -8.5) equal to 8.200609733 and -8.200609733.Subproblem 1
X + -8.5 = 8.200609733 Simplifying X + -8.5 = 8.200609733 Reorder the terms: -8.5 + X = 8.200609733 Solving -8.5 + X = 8.200609733 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 = 8.200609733 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + X = 8.200609733 + 8.5 X = 8.200609733 + 8.5 Combine like terms: 8.200609733 + 8.5 = 16.700609733 X = 16.700609733 Simplifying X = 16.700609733Subproblem 2
X + -8.5 = -8.200609733 Simplifying X + -8.5 = -8.200609733 Reorder the terms: -8.5 + X = -8.200609733 Solving -8.5 + X = -8.200609733 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 = -8.200609733 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + X = -8.200609733 + 8.5 X = -8.200609733 + 8.5 Combine like terms: -8.200609733 + 8.5 = 0.299390267 X = 0.299390267 Simplifying X = 0.299390267Solution
The solution to the problem is based on the solutions from the subproblems. X = {16.700609733, 0.299390267}
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