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Simplifying x(x + -6) = 108 Reorder the terms: x(-6 + x) = 108 (-6 * x + x * x) = 108 (-6x + x2) = 108 Solving -6x + x2 = 108 Solving for variable 'x'. Reorder the terms: -108 + -6x + x2 = 108 + -108 Combine like terms: 108 + -108 = 0 -108 + -6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '108' to each side of the equation. -108 + -6x + 108 + x2 = 0 + 108 Reorder the terms: -108 + 108 + -6x + x2 = 0 + 108 Combine like terms: -108 + 108 = 0 0 + -6x + x2 = 0 + 108 -6x + x2 = 0 + 108 Combine like terms: 0 + 108 = 108 -6x + x2 = 108 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 108 + 9 Reorder the terms: 9 + -6x + x2 = 108 + 9 Combine like terms: 108 + 9 = 117 9 + -6x + x2 = 117 Factor a perfect square on the left side: (x + -3)(x + -3) = 117 Calculate the square root of the right side: 10.816653826 Break this problem into two subproblems by setting (x + -3) equal to 10.816653826 and -10.816653826.Subproblem 1
x + -3 = 10.816653826 Simplifying x + -3 = 10.816653826 Reorder the terms: -3 + x = 10.816653826 Solving -3 + x = 10.816653826 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 10.816653826 + 3 Combine like terms: -3 + 3 = 0 0 + x = 10.816653826 + 3 x = 10.816653826 + 3 Combine like terms: 10.816653826 + 3 = 13.816653826 x = 13.816653826 Simplifying x = 13.816653826Subproblem 2
x + -3 = -10.816653826 Simplifying x + -3 = -10.816653826 Reorder the terms: -3 + x = -10.816653826 Solving -3 + x = -10.816653826 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -10.816653826 + 3 Combine like terms: -3 + 3 = 0 0 + x = -10.816653826 + 3 x = -10.816653826 + 3 Combine like terms: -10.816653826 + 3 = -7.816653826 x = -7.816653826 Simplifying x = -7.816653826Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.816653826, -7.816653826}
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