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Simplifying x + 16 = x(12 + x) Reorder the terms: 16 + x = x(12 + x) 16 + x = (12 * x + x * x) 16 + x = (12x + x2) Solving 16 + x = 12x + x2 Solving for variable 'x'. Combine like terms: x + -12x = -11x 16 + -11x + -1x2 = 12x + x2 + -12x + -1x2 Reorder the terms: 16 + -11x + -1x2 = 12x + -12x + x2 + -1x2 Combine like terms: 12x + -12x = 0 16 + -11x + -1x2 = 0 + x2 + -1x2 16 + -11x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 16 + -11x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -16 + 11x + x2 = 0 Move the constant term to the right: Add '16' to each side of the equation. -16 + 11x + 16 + x2 = 0 + 16 Reorder the terms: -16 + 16 + 11x + x2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + 11x + x2 = 0 + 16 11x + x2 = 0 + 16 Combine like terms: 0 + 16 = 16 11x + x2 = 16 The x term is 11x. Take half its coefficient (5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. 11x + 30.25 + x2 = 16 + 30.25 Reorder the terms: 30.25 + 11x + x2 = 16 + 30.25 Combine like terms: 16 + 30.25 = 46.25 30.25 + 11x + x2 = 46.25 Factor a perfect square on the left side: (x + 5.5)(x + 5.5) = 46.25 Calculate the square root of the right side: 6.800735254 Break this problem into two subproblems by setting (x + 5.5) equal to 6.800735254 and -6.800735254.Subproblem 1
x + 5.5 = 6.800735254 Simplifying x + 5.5 = 6.800735254 Reorder the terms: 5.5 + x = 6.800735254 Solving 5.5 + x = 6.800735254 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = 6.800735254 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 6.800735254 + -5.5 x = 6.800735254 + -5.5 Combine like terms: 6.800735254 + -5.5 = 1.300735254 x = 1.300735254 Simplifying x = 1.300735254Subproblem 2
x + 5.5 = -6.800735254 Simplifying x + 5.5 = -6.800735254 Reorder the terms: 5.5 + x = -6.800735254 Solving 5.5 + x = -6.800735254 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = -6.800735254 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -6.800735254 + -5.5 x = -6.800735254 + -5.5 Combine like terms: -6.800735254 + -5.5 = -12.300735254 x = -12.300735254 Simplifying x = -12.300735254Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.300735254, -12.300735254}
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