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Simplifying 6x + 12 = x2 + -12 Reorder the terms: 12 + 6x = x2 + -12 Reorder the terms: 12 + 6x = -12 + x2 Solving 12 + 6x = -12 + x2 Solving for variable 'x'. Reorder the terms: 12 + 12 + 6x + -1x2 = -12 + x2 + 12 + -1x2 Combine like terms: 12 + 12 = 24 24 + 6x + -1x2 = -12 + x2 + 12 + -1x2 Reorder the terms: 24 + 6x + -1x2 = -12 + 12 + x2 + -1x2 Combine like terms: -12 + 12 = 0 24 + 6x + -1x2 = 0 + x2 + -1x2 24 + 6x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 24 + 6x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -24 + -6x + x2 = 0 Move the constant term to the right: Add '24' to each side of the equation. -24 + -6x + 24 + x2 = 0 + 24 Reorder the terms: -24 + 24 + -6x + x2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + -6x + x2 = 0 + 24 -6x + x2 = 0 + 24 Combine like terms: 0 + 24 = 24 -6x + x2 = 24 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 = 24 + 9 Reorder the terms: 9 + -6x + x2 = 24 + 9 Combine like terms: 24 + 9 = 33 9 + -6x + x2 = 33 Factor a perfect square on the left side: (x + -3)(x + -3) = 33 Calculate the square root of the right side: 5.744562647 Break this problem into two subproblems by setting (x + -3) equal to 5.744562647 and -5.744562647.Subproblem 1
x + -3 = 5.744562647 Simplifying x + -3 = 5.744562647 Reorder the terms: -3 + x = 5.744562647 Solving -3 + x = 5.744562647 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 = 5.744562647 + 3 Combine like terms: -3 + 3 = 0 0 + x = 5.744562647 + 3 x = 5.744562647 + 3 Combine like terms: 5.744562647 + 3 = 8.744562647 x = 8.744562647 Simplifying x = 8.744562647Subproblem 2
x + -3 = -5.744562647 Simplifying x + -3 = -5.744562647 Reorder the terms: -3 + x = -5.744562647 Solving -3 + x = -5.744562647 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 = -5.744562647 + 3 Combine like terms: -3 + 3 = 0 0 + x = -5.744562647 + 3 x = -5.744562647 + 3 Combine like terms: -5.744562647 + 3 = -2.744562647 x = -2.744562647 Simplifying x = -2.744562647Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.744562647, -2.744562647}
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