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Simplifying x2 + -10x = 108 Reorder the terms: -10x + x2 = 108 Solving -10x + x2 = 108 Solving for variable 'x'. Reorder the terms: -108 + -10x + x2 = 108 + -108 Combine like terms: 108 + -108 = 0 -108 + -10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '108' to each side of the equation. -108 + -10x + 108 + x2 = 0 + 108 Reorder the terms: -108 + 108 + -10x + x2 = 0 + 108 Combine like terms: -108 + 108 = 0 0 + -10x + x2 = 0 + 108 -10x + x2 = 0 + 108 Combine like terms: 0 + 108 = 108 -10x + x2 = 108 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 = 108 + 25 Reorder the terms: 25 + -10x + x2 = 108 + 25 Combine like terms: 108 + 25 = 133 25 + -10x + x2 = 133 Factor a perfect square on the left side: (x + -5)(x + -5) = 133 Calculate the square root of the right side: 11.532562595 Break this problem into two subproblems by setting (x + -5) equal to 11.532562595 and -11.532562595.Subproblem 1
x + -5 = 11.532562595 Simplifying x + -5 = 11.532562595 Reorder the terms: -5 + x = 11.532562595 Solving -5 + x = 11.532562595 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 = 11.532562595 + 5 Combine like terms: -5 + 5 = 0 0 + x = 11.532562595 + 5 x = 11.532562595 + 5 Combine like terms: 11.532562595 + 5 = 16.532562595 x = 16.532562595 Simplifying x = 16.532562595Subproblem 2
x + -5 = -11.532562595 Simplifying x + -5 = -11.532562595 Reorder the terms: -5 + x = -11.532562595 Solving -5 + x = -11.532562595 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 = -11.532562595 + 5 Combine like terms: -5 + 5 = 0 0 + x = -11.532562595 + 5 x = -11.532562595 + 5 Combine like terms: -11.532562595 + 5 = -6.532562595 x = -6.532562595 Simplifying x = -6.532562595Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.532562595, -6.532562595}
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