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Simplifying x2 + 10x + -108 = 0 Reorder the terms: -108 + 10x + x2 = 0 Solving -108 + 10x + x2 = 0 Solving for variable 'x'. 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 = 6.532562595 x = 6.532562595 Simplifying x = 6.532562595Subproblem 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 = -16.532562595 x = -16.532562595 Simplifying x = -16.532562595Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.532562595, -16.532562595}
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