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Simplifying x2 + -12x + -204 = 0 Reorder the terms: -204 + -12x + x2 = 0 Solving -204 + -12x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '204' to each side of the equation. -204 + -12x + 204 + x2 = 0 + 204 Reorder the terms: -204 + 204 + -12x + x2 = 0 + 204 Combine like terms: -204 + 204 = 0 0 + -12x + x2 = 0 + 204 -12x + x2 = 0 + 204 Combine like terms: 0 + 204 = 204 -12x + x2 = 204 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 = 204 + 36 Reorder the terms: 36 + -12x + x2 = 204 + 36 Combine like terms: 204 + 36 = 240 36 + -12x + x2 = 240 Factor a perfect square on the left side: (x + -6)(x + -6) = 240 Calculate the square root of the right side: 15.491933385 Break this problem into two subproblems by setting (x + -6) equal to 15.491933385 and -15.491933385.Subproblem 1
x + -6 = 15.491933385 Simplifying x + -6 = 15.491933385 Reorder the terms: -6 + x = 15.491933385 Solving -6 + x = 15.491933385 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 = 15.491933385 + 6 Combine like terms: -6 + 6 = 0 0 + x = 15.491933385 + 6 x = 15.491933385 + 6 Combine like terms: 15.491933385 + 6 = 21.491933385 x = 21.491933385 Simplifying x = 21.491933385Subproblem 2
x + -6 = -15.491933385 Simplifying x + -6 = -15.491933385 Reorder the terms: -6 + x = -15.491933385 Solving -6 + x = -15.491933385 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 = -15.491933385 + 6 Combine like terms: -6 + 6 = 0 0 + x = -15.491933385 + 6 x = -15.491933385 + 6 Combine like terms: -15.491933385 + 6 = -9.491933385 x = -9.491933385 Simplifying x = -9.491933385Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.491933385, -9.491933385}
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