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Simplifying x2 + -12x + -228 = 0 Reorder the terms: -228 + -12x + x2 = 0 Solving -228 + -12x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '228' to each side of the equation. -228 + -12x + 228 + x2 = 0 + 228 Reorder the terms: -228 + 228 + -12x + x2 = 0 + 228 Combine like terms: -228 + 228 = 0 0 + -12x + x2 = 0 + 228 -12x + x2 = 0 + 228 Combine like terms: 0 + 228 = 228 -12x + x2 = 228 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 = 228 + 36 Reorder the terms: 36 + -12x + x2 = 228 + 36 Combine like terms: 228 + 36 = 264 36 + -12x + x2 = 264 Factor a perfect square on the left side: (x + -6)(x + -6) = 264 Calculate the square root of the right side: 16.248076809 Break this problem into two subproblems by setting (x + -6) equal to 16.248076809 and -16.248076809.Subproblem 1
x + -6 = 16.248076809 Simplifying x + -6 = 16.248076809 Reorder the terms: -6 + x = 16.248076809 Solving -6 + x = 16.248076809 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 = 16.248076809 + 6 Combine like terms: -6 + 6 = 0 0 + x = 16.248076809 + 6 x = 16.248076809 + 6 Combine like terms: 16.248076809 + 6 = 22.248076809 x = 22.248076809 Simplifying x = 22.248076809Subproblem 2
x + -6 = -16.248076809 Simplifying x + -6 = -16.248076809 Reorder the terms: -6 + x = -16.248076809 Solving -6 + x = -16.248076809 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 = -16.248076809 + 6 Combine like terms: -6 + 6 = 0 0 + x = -16.248076809 + 6 x = -16.248076809 + 6 Combine like terms: -16.248076809 + 6 = -10.248076809 x = -10.248076809 Simplifying x = -10.248076809Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.248076809, -10.248076809}
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