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Simplifying x(12 + x) = 2x + 8 (12 * x + x * x) = 2x + 8 (12x + x2) = 2x + 8 Reorder the terms: 12x + x2 = 8 + 2x Solving 12x + x2 = 8 + 2x Solving for variable 'x'. Reorder the terms: -8 + 12x + -2x + x2 = 8 + 2x + -8 + -2x Combine like terms: 12x + -2x = 10x -8 + 10x + x2 = 8 + 2x + -8 + -2x Reorder the terms: -8 + 10x + x2 = 8 + -8 + 2x + -2x Combine like terms: 8 + -8 = 0 -8 + 10x + x2 = 0 + 2x + -2x -8 + 10x + x2 = 2x + -2x Combine like terms: 2x + -2x = 0 -8 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + 10x + 8 + x2 = 0 + 8 Reorder the terms: -8 + 8 + 10x + x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 10x + x2 = 0 + 8 10x + x2 = 0 + 8 Combine like terms: 0 + 8 = 8 10x + x2 = 8 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = 8 + 25 Reorder the terms: 25 + 10x + x2 = 8 + 25 Combine like terms: 8 + 25 = 33 25 + 10x + x2 = 33 Factor a perfect square on the left side: (x + 5)(x + 5) = 33 Calculate the square root of the right side: 5.744562647 Break this problem into two subproblems by setting (x + 5) equal to 5.744562647 and -5.744562647.Subproblem 1
x + 5 = 5.744562647 Simplifying x + 5 = 5.744562647 Reorder the terms: 5 + x = 5.744562647 Solving 5 + x = 5.744562647 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 5.744562647 + -5 Combine like terms: 5 + -5 = 0 0 + x = 5.744562647 + -5 x = 5.744562647 + -5 Combine like terms: 5.744562647 + -5 = 0.744562647 x = 0.744562647 Simplifying x = 0.744562647Subproblem 2
x + 5 = -5.744562647 Simplifying x + 5 = -5.744562647 Reorder the terms: 5 + x = -5.744562647 Solving 5 + x = -5.744562647 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -5.744562647 + -5 Combine like terms: 5 + -5 = 0 0 + x = -5.744562647 + -5 x = -5.744562647 + -5 Combine like terms: -5.744562647 + -5 = -10.744562647 x = -10.744562647 Simplifying x = -10.744562647Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.744562647, -10.744562647}
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