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Simplifying (x + -6)(x + -6) = 108 Reorder the terms: (-6 + x)(x + -6) = 108 Reorder the terms: (-6 + x)(-6 + x) = 108 Multiply (-6 + x) * (-6 + x) (-6(-6 + x) + x(-6 + x)) = 108 ((-6 * -6 + x * -6) + x(-6 + x)) = 108 ((36 + -6x) + x(-6 + x)) = 108 (36 + -6x + (-6 * x + x * x)) = 108 (36 + -6x + (-6x + x2)) = 108 Combine like terms: -6x + -6x = -12x (36 + -12x + x2) = 108 Solving 36 + -12x + x2 = 108 Solving for variable 'x'. Reorder the terms: 36 + -108 + -12x + x2 = 108 + -108 Combine like terms: 36 + -108 = -72 -72 + -12x + x2 = 108 + -108 Combine like terms: 108 + -108 = 0 -72 + -12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '72' to each side of the equation. -72 + -12x + 72 + x2 = 0 + 72 Reorder the terms: -72 + 72 + -12x + x2 = 0 + 72 Combine like terms: -72 + 72 = 0 0 + -12x + x2 = 0 + 72 -12x + x2 = 0 + 72 Combine like terms: 0 + 72 = 72 -12x + x2 = 72 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = 72 + 36 Reorder the terms: 36 + -12x + x2 = 72 + 36 Combine like terms: 72 + 36 = 108 36 + -12x + x2 = 108 Factor a perfect square on the left side: (x + -6)(x + -6) = 108 Calculate the square root of the right side: 10.392304845 Break this problem into two subproblems by setting (x + -6) equal to 10.392304845 and -10.392304845.Subproblem 1
x + -6 = 10.392304845 Simplifying x + -6 = 10.392304845 Reorder the terms: -6 + x = 10.392304845 Solving -6 + x = 10.392304845 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 10.392304845 + 6 Combine like terms: -6 + 6 = 0 0 + x = 10.392304845 + 6 x = 10.392304845 + 6 Combine like terms: 10.392304845 + 6 = 16.392304845 x = 16.392304845 Simplifying x = 16.392304845Subproblem 2
x + -6 = -10.392304845 Simplifying x + -6 = -10.392304845 Reorder the terms: -6 + x = -10.392304845 Solving -6 + x = -10.392304845 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -10.392304845 + 6 Combine like terms: -6 + 6 = 0 0 + x = -10.392304845 + 6 x = -10.392304845 + 6 Combine like terms: -10.392304845 + 6 = -4.392304845 x = -4.392304845 Simplifying x = -4.392304845Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.392304845, -4.392304845}
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