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Simplifying (x + -5)(x + 5) + 12x = 6x + 12 Reorder the terms: (-5 + x)(x + 5) + 12x = 6x + 12 Reorder the terms: (-5 + x)(5 + x) + 12x = 6x + 12 Multiply (-5 + x) * (5 + x) (-5(5 + x) + x(5 + x)) + 12x = 6x + 12 ((5 * -5 + x * -5) + x(5 + x)) + 12x = 6x + 12 ((-25 + -5x) + x(5 + x)) + 12x = 6x + 12 (-25 + -5x + (5 * x + x * x)) + 12x = 6x + 12 (-25 + -5x + (5x + x2)) + 12x = 6x + 12 Combine like terms: -5x + 5x = 0 (-25 + 0 + x2) + 12x = 6x + 12 (-25 + x2) + 12x = 6x + 12 Reorder the terms: -25 + 12x + x2 = 6x + 12 Reorder the terms: -25 + 12x + x2 = 12 + 6x Solving -25 + 12x + x2 = 12 + 6x Solving for variable 'x'. Reorder the terms: -25 + -12 + 12x + -6x + x2 = 12 + 6x + -12 + -6x Combine like terms: -25 + -12 = -37 -37 + 12x + -6x + x2 = 12 + 6x + -12 + -6x Combine like terms: 12x + -6x = 6x -37 + 6x + x2 = 12 + 6x + -12 + -6x Reorder the terms: -37 + 6x + x2 = 12 + -12 + 6x + -6x Combine like terms: 12 + -12 = 0 -37 + 6x + x2 = 0 + 6x + -6x -37 + 6x + x2 = 6x + -6x Combine like terms: 6x + -6x = 0 -37 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '37' to each side of the equation. -37 + 6x + 37 + x2 = 0 + 37 Reorder the terms: -37 + 37 + 6x + x2 = 0 + 37 Combine like terms: -37 + 37 = 0 0 + 6x + x2 = 0 + 37 6x + x2 = 0 + 37 Combine like terms: 0 + 37 = 37 6x + x2 = 37 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 37 + 9 Reorder the terms: 9 + 6x + x2 = 37 + 9 Combine like terms: 37 + 9 = 46 9 + 6x + x2 = 46 Factor a perfect square on the left side: (x + 3)(x + 3) = 46 Calculate the square root of the right side: 6.782329983 Break this problem into two subproblems by setting (x + 3) equal to 6.782329983 and -6.782329983.Subproblem 1
x + 3 = 6.782329983 Simplifying x + 3 = 6.782329983 Reorder the terms: 3 + x = 6.782329983 Solving 3 + x = 6.782329983 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 6.782329983 + -3 Combine like terms: 3 + -3 = 0 0 + x = 6.782329983 + -3 x = 6.782329983 + -3 Combine like terms: 6.782329983 + -3 = 3.782329983 x = 3.782329983 Simplifying x = 3.782329983Subproblem 2
x + 3 = -6.782329983 Simplifying x + 3 = -6.782329983 Reorder the terms: 3 + x = -6.782329983 Solving 3 + x = -6.782329983 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -6.782329983 + -3 Combine like terms: 3 + -3 = 0 0 + x = -6.782329983 + -3 x = -6.782329983 + -3 Combine like terms: -6.782329983 + -3 = -9.782329983 x = -9.782329983 Simplifying x = -9.782329983Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.782329983, -9.782329983}
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