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Simplifying x2 + -10x + -407 = 0 Reorder the terms: -407 + -10x + x2 = 0 Solving -407 + -10x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '407' to each side of the equation. -407 + -10x + 407 + x2 = 0 + 407 Reorder the terms: -407 + 407 + -10x + x2 = 0 + 407 Combine like terms: -407 + 407 = 0 0 + -10x + x2 = 0 + 407 -10x + x2 = 0 + 407 Combine like terms: 0 + 407 = 407 -10x + x2 = 407 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 = 407 + 25 Reorder the terms: 25 + -10x + x2 = 407 + 25 Combine like terms: 407 + 25 = 432 25 + -10x + x2 = 432 Factor a perfect square on the left side: (x + -5)(x + -5) = 432 Calculate the square root of the right side: 20.784609691 Break this problem into two subproblems by setting (x + -5) equal to 20.784609691 and -20.784609691.Subproblem 1
x + -5 = 20.784609691 Simplifying x + -5 = 20.784609691 Reorder the terms: -5 + x = 20.784609691 Solving -5 + x = 20.784609691 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 = 20.784609691 + 5 Combine like terms: -5 + 5 = 0 0 + x = 20.784609691 + 5 x = 20.784609691 + 5 Combine like terms: 20.784609691 + 5 = 25.784609691 x = 25.784609691 Simplifying x = 25.784609691Subproblem 2
x + -5 = -20.784609691 Simplifying x + -5 = -20.784609691 Reorder the terms: -5 + x = -20.784609691 Solving -5 + x = -20.784609691 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 = -20.784609691 + 5 Combine like terms: -5 + 5 = 0 0 + x = -20.784609691 + 5 x = -20.784609691 + 5 Combine like terms: -20.784609691 + 5 = -15.784609691 x = -15.784609691 Simplifying x = -15.784609691Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.784609691, -15.784609691}
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