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Simplifying (x + 4) * 2 = x(x + 12) Reorder the terms: (4 + x) * 2 = x(x + 12) Reorder the terms for easier multiplication: 2(4 + x) = x(x + 12) (4 * 2 + x * 2) = x(x + 12) (8 + 2x) = x(x + 12) Reorder the terms: 8 + 2x = x(12 + x) 8 + 2x = (12 * x + x * x) 8 + 2x = (12x + x2) Solving 8 + 2x = 12x + x2 Solving for variable 'x'. Combine like terms: 2x + -12x = -10x 8 + -10x + -1x2 = 12x + x2 + -12x + -1x2 Reorder the terms: 8 + -10x + -1x2 = 12x + -12x + x2 + -1x2 Combine like terms: 12x + -12x = 0 8 + -10x + -1x2 = 0 + x2 + -1x2 8 + -10x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 8 + -10x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -8 + 10x + x2 = 0 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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