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Simplifying x2 + -10x + -25 = -17 Reorder the terms: -25 + -10x + x2 = -17 Solving -25 + -10x + x2 = -17 Solving for variable 'x'. Reorder the terms: -25 + 17 + -10x + x2 = -17 + 17 Combine like terms: -25 + 17 = -8 -8 + -10x + x2 = -17 + 17 Combine like terms: -17 + 17 = 0 -8 + -10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + -10x + 8 + x2 = 0 + 8 Reorder the terms: -8 + 8 + -10x + x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -10x + x2 = 0 + 8 -10x + x2 = 0 + 8 Combine like terms: 0 + 8 = 8 -10x + x2 = 8 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = 8 + 25 Reorder the terms: 25 + -10x + x2 = 8 + 25 Combine like terms: 8 + 25 = 33 25 + -10x + x2 = 33 Factor a perfect square on the left side: (x + -5)(x + -5) = 33 Calculate the square root of the right side: 5.744562647 Break this problem into two subproblems by setting (x + -5) equal to 5.744562647 and -5.744562647.Subproblem 1
x + -5 = 5.744562647 Simplifying x + -5 = 5.744562647 Reorder the terms: -5 + x = 5.744562647 Solving -5 + x = 5.744562647 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 5.744562647 + 5 Combine like terms: -5 + 5 = 0 0 + x = 5.744562647 + 5 x = 5.744562647 + 5 Combine like terms: 5.744562647 + 5 = 10.744562647 x = 10.744562647 Simplifying x = 10.744562647Subproblem 2
x + -5 = -5.744562647 Simplifying x + -5 = -5.744562647 Reorder the terms: -5 + x = -5.744562647 Solving -5 + x = -5.744562647 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -5.744562647 + 5 Combine like terms: -5 + 5 = 0 0 + x = -5.744562647 + 5 x = -5.744562647 + 5 Combine like terms: -5.744562647 + 5 = -0.744562647 x = -0.744562647 Simplifying x = -0.744562647Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.744562647, -0.744562647}
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