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Simplifying 16x + 208 = x2 + 6x + 9 Reorder the terms: 208 + 16x = x2 + 6x + 9 Reorder the terms: 208 + 16x = 9 + 6x + x2 Solving 208 + 16x = 9 + 6x + x2 Solving for variable 'x'. Reorder the terms: 208 + -9 + 16x + -6x + -1x2 = 9 + 6x + x2 + -9 + -6x + -1x2 Combine like terms: 208 + -9 = 199 199 + 16x + -6x + -1x2 = 9 + 6x + x2 + -9 + -6x + -1x2 Combine like terms: 16x + -6x = 10x 199 + 10x + -1x2 = 9 + 6x + x2 + -9 + -6x + -1x2 Reorder the terms: 199 + 10x + -1x2 = 9 + -9 + 6x + -6x + x2 + -1x2 Combine like terms: 9 + -9 = 0 199 + 10x + -1x2 = 0 + 6x + -6x + x2 + -1x2 199 + 10x + -1x2 = 6x + -6x + x2 + -1x2 Combine like terms: 6x + -6x = 0 199 + 10x + -1x2 = 0 + x2 + -1x2 199 + 10x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 199 + 10x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -199 + -10x + x2 = 0 Move the constant term to the right: Add '199' to each side of the equation. -199 + -10x + 199 + x2 = 0 + 199 Reorder the terms: -199 + 199 + -10x + x2 = 0 + 199 Combine like terms: -199 + 199 = 0 0 + -10x + x2 = 0 + 199 -10x + x2 = 0 + 199 Combine like terms: 0 + 199 = 199 -10x + x2 = 199 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 = 199 + 25 Reorder the terms: 25 + -10x + x2 = 199 + 25 Combine like terms: 199 + 25 = 224 25 + -10x + x2 = 224 Factor a perfect square on the left side: (x + -5)(x + -5) = 224 Calculate the square root of the right side: 14.966629547 Break this problem into two subproblems by setting (x + -5) equal to 14.966629547 and -14.966629547.Subproblem 1
x + -5 = 14.966629547 Simplifying x + -5 = 14.966629547 Reorder the terms: -5 + x = 14.966629547 Solving -5 + x = 14.966629547 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 = 14.966629547 + 5 Combine like terms: -5 + 5 = 0 0 + x = 14.966629547 + 5 x = 14.966629547 + 5 Combine like terms: 14.966629547 + 5 = 19.966629547 x = 19.966629547 Simplifying x = 19.966629547Subproblem 2
x + -5 = -14.966629547 Simplifying x + -5 = -14.966629547 Reorder the terms: -5 + x = -14.966629547 Solving -5 + x = -14.966629547 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 = -14.966629547 + 5 Combine like terms: -5 + 5 = 0 0 + x = -14.966629547 + 5 x = -14.966629547 + 5 Combine like terms: -14.966629547 + 5 = -9.966629547 x = -9.966629547 Simplifying x = -9.966629547Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.966629547, -9.966629547}
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