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Simplifying 2x + -12 + 4x = x2 + -4x + 6 Reorder the terms: -12 + 2x + 4x = x2 + -4x + 6 Combine like terms: 2x + 4x = 6x -12 + 6x = x2 + -4x + 6 Reorder the terms: -12 + 6x = 6 + -4x + x2 Solving -12 + 6x = 6 + -4x + x2 Solving for variable 'x'. Reorder the terms: -12 + -6 + 6x + 4x + -1x2 = 6 + -4x + x2 + -6 + 4x + -1x2 Combine like terms: -12 + -6 = -18 -18 + 6x + 4x + -1x2 = 6 + -4x + x2 + -6 + 4x + -1x2 Combine like terms: 6x + 4x = 10x -18 + 10x + -1x2 = 6 + -4x + x2 + -6 + 4x + -1x2 Reorder the terms: -18 + 10x + -1x2 = 6 + -6 + -4x + 4x + x2 + -1x2 Combine like terms: 6 + -6 = 0 -18 + 10x + -1x2 = 0 + -4x + 4x + x2 + -1x2 -18 + 10x + -1x2 = -4x + 4x + x2 + -1x2 Combine like terms: -4x + 4x = 0 -18 + 10x + -1x2 = 0 + x2 + -1x2 -18 + 10x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -18 + 10x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 18 + -10x + x2 = 0 Move the constant term to the right: Add '-18' to each side of the equation. 18 + -10x + -18 + x2 = 0 + -18 Reorder the terms: 18 + -18 + -10x + x2 = 0 + -18 Combine like terms: 18 + -18 = 0 0 + -10x + x2 = 0 + -18 -10x + x2 = 0 + -18 Combine like terms: 0 + -18 = -18 -10x + x2 = -18 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 = -18 + 25 Reorder the terms: 25 + -10x + x2 = -18 + 25 Combine like terms: -18 + 25 = 7 25 + -10x + x2 = 7 Factor a perfect square on the left side: (x + -5)(x + -5) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (x + -5) equal to 2.645751311 and -2.645751311.Subproblem 1
x + -5 = 2.645751311 Simplifying x + -5 = 2.645751311 Reorder the terms: -5 + x = 2.645751311 Solving -5 + x = 2.645751311 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 = 2.645751311 + 5 Combine like terms: -5 + 5 = 0 0 + x = 2.645751311 + 5 x = 2.645751311 + 5 Combine like terms: 2.645751311 + 5 = 7.645751311 x = 7.645751311 Simplifying x = 7.645751311Subproblem 2
x + -5 = -2.645751311 Simplifying x + -5 = -2.645751311 Reorder the terms: -5 + x = -2.645751311 Solving -5 + x = -2.645751311 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 = -2.645751311 + 5 Combine like terms: -5 + 5 = 0 0 + x = -2.645751311 + 5 x = -2.645751311 + 5 Combine like terms: -2.645751311 + 5 = 2.354248689 x = 2.354248689 Simplifying x = 2.354248689Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.645751311, 2.354248689}
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