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Simplifying (x + -2)(x + 2) + 6 = 6x Reorder the terms: (-2 + x)(x + 2) + 6 = 6x Reorder the terms: (-2 + x)(2 + x) + 6 = 6x Multiply (-2 + x) * (2 + x) (-2(2 + x) + x(2 + x)) + 6 = 6x ((2 * -2 + x * -2) + x(2 + x)) + 6 = 6x ((-4 + -2x) + x(2 + x)) + 6 = 6x (-4 + -2x + (2 * x + x * x)) + 6 = 6x (-4 + -2x + (2x + x2)) + 6 = 6x Combine like terms: -2x + 2x = 0 (-4 + 0 + x2) + 6 = 6x (-4 + x2) + 6 = 6x Reorder the terms: -4 + 6 + x2 = 6x Combine like terms: -4 + 6 = 2 2 + x2 = 6x Solving 2 + x2 = 6x Solving for variable 'x'. Reorder the terms: 2 + -6x + x2 = 6x + -6x Combine like terms: 6x + -6x = 0 2 + -6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + -6x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + -6x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -6x + x2 = 0 + -2 -6x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 -6x + x2 = -2 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 = -2 + 9 Reorder the terms: 9 + -6x + x2 = -2 + 9 Combine like terms: -2 + 9 = 7 9 + -6x + x2 = 7 Factor a perfect square on the left side: (x + -3)(x + -3) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (x + -3) equal to 2.645751311 and -2.645751311.Subproblem 1
x + -3 = 2.645751311 Simplifying x + -3 = 2.645751311 Reorder the terms: -3 + x = 2.645751311 Solving -3 + x = 2.645751311 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 = 2.645751311 + 3 Combine like terms: -3 + 3 = 0 0 + x = 2.645751311 + 3 x = 2.645751311 + 3 Combine like terms: 2.645751311 + 3 = 5.645751311 x = 5.645751311 Simplifying x = 5.645751311Subproblem 2
x + -3 = -2.645751311 Simplifying x + -3 = -2.645751311 Reorder the terms: -3 + x = -2.645751311 Solving -3 + x = -2.645751311 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 = -2.645751311 + 3 Combine like terms: -3 + 3 = 0 0 + x = -2.645751311 + 3 x = -2.645751311 + 3 Combine like terms: -2.645751311 + 3 = 0.354248689 x = 0.354248689 Simplifying x = 0.354248689Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.645751311, 0.354248689}
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