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Simplifying X2 + -8X = 17 Reorder the terms: -8X + X2 = 17 Solving -8X + X2 = 17 Solving for variable 'X'. Reorder the terms: -17 + -8X + X2 = 17 + -17 Combine like terms: 17 + -17 = 0 -17 + -8X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '17' to each side of the equation. -17 + -8X + 17 + X2 = 0 + 17 Reorder the terms: -17 + 17 + -8X + X2 = 0 + 17 Combine like terms: -17 + 17 = 0 0 + -8X + X2 = 0 + 17 -8X + X2 = 0 + 17 Combine like terms: 0 + 17 = 17 -8X + X2 = 17 The X term is -8X. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8X + 16 + X2 = 17 + 16 Reorder the terms: 16 + -8X + X2 = 17 + 16 Combine like terms: 17 + 16 = 33 16 + -8X + X2 = 33 Factor a perfect square on the left side: (X + -4)(X + -4) = 33 Calculate the square root of the right side: 5.744562647 Break this problem into two subproblems by setting (X + -4) equal to 5.744562647 and -5.744562647.Subproblem 1
X + -4 = 5.744562647 Simplifying X + -4 = 5.744562647 Reorder the terms: -4 + X = 5.744562647 Solving -4 + X = 5.744562647 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + X = 5.744562647 + 4 Combine like terms: -4 + 4 = 0 0 + X = 5.744562647 + 4 X = 5.744562647 + 4 Combine like terms: 5.744562647 + 4 = 9.744562647 X = 9.744562647 Simplifying X = 9.744562647Subproblem 2
X + -4 = -5.744562647 Simplifying X + -4 = -5.744562647 Reorder the terms: -4 + X = -5.744562647 Solving -4 + X = -5.744562647 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + X = -5.744562647 + 4 Combine like terms: -4 + 4 = 0 0 + X = -5.744562647 + 4 X = -5.744562647 + 4 Combine like terms: -5.744562647 + 4 = -1.744562647 X = -1.744562647 Simplifying X = -1.744562647Solution
The solution to the problem is based on the solutions from the subproblems. X = {9.744562647, -1.744562647}
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