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Simplifying 2x2 + -12 + 4x = (x + -2)(x + -2) + 2 Reorder the terms: -12 + 4x + 2x2 = (x + -2)(x + -2) + 2 Reorder the terms: -12 + 4x + 2x2 = (-2 + x)(x + -2) + 2 Reorder the terms: -12 + 4x + 2x2 = (-2 + x)(-2 + x) + 2 Multiply (-2 + x) * (-2 + x) -12 + 4x + 2x2 = (-2(-2 + x) + x(-2 + x)) + 2 -12 + 4x + 2x2 = ((-2 * -2 + x * -2) + x(-2 + x)) + 2 -12 + 4x + 2x2 = ((4 + -2x) + x(-2 + x)) + 2 -12 + 4x + 2x2 = (4 + -2x + (-2 * x + x * x)) + 2 -12 + 4x + 2x2 = (4 + -2x + (-2x + x2)) + 2 Combine like terms: -2x + -2x = -4x -12 + 4x + 2x2 = (4 + -4x + x2) + 2 Reorder the terms: -12 + 4x + 2x2 = 4 + 2 + -4x + x2 Combine like terms: 4 + 2 = 6 -12 + 4x + 2x2 = 6 + -4x + x2 Solving -12 + 4x + 2x2 = 6 + -4x + x2 Solving for variable 'x'. Reorder the terms: -12 + -6 + 4x + 4x + 2x2 + -1x2 = 6 + -4x + x2 + -6 + 4x + -1x2 Combine like terms: -12 + -6 = -18 -18 + 4x + 4x + 2x2 + -1x2 = 6 + -4x + x2 + -6 + 4x + -1x2 Combine like terms: 4x + 4x = 8x -18 + 8x + 2x2 + -1x2 = 6 + -4x + x2 + -6 + 4x + -1x2 Combine like terms: 2x2 + -1x2 = 1x2 -18 + 8x + 1x2 = 6 + -4x + x2 + -6 + 4x + -1x2 Reorder the terms: -18 + 8x + 1x2 = 6 + -6 + -4x + 4x + x2 + -1x2 Combine like terms: 6 + -6 = 0 -18 + 8x + 1x2 = 0 + -4x + 4x + x2 + -1x2 -18 + 8x + 1x2 = -4x + 4x + x2 + -1x2 Combine like terms: -4x + 4x = 0 -18 + 8x + 1x2 = 0 + x2 + -1x2 -18 + 8x + 1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -18 + 8x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '18' to each side of the equation. -18 + 8x + 18 + x2 = 0 + 18 Reorder the terms: -18 + 18 + 8x + x2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + 8x + x2 = 0 + 18 8x + x2 = 0 + 18 Combine like terms: 0 + 18 = 18 8x + x2 = 18 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = 18 + 16 Reorder the terms: 16 + 8x + x2 = 18 + 16 Combine like terms: 18 + 16 = 34 16 + 8x + x2 = 34 Factor a perfect square on the left side: (x + 4)(x + 4) = 34 Calculate the square root of the right side: 5.830951895 Break this problem into two subproblems by setting (x + 4) equal to 5.830951895 and -5.830951895.Subproblem 1
x + 4 = 5.830951895 Simplifying x + 4 = 5.830951895 Reorder the terms: 4 + x = 5.830951895 Solving 4 + x = 5.830951895 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 5.830951895 + -4 Combine like terms: 4 + -4 = 0 0 + x = 5.830951895 + -4 x = 5.830951895 + -4 Combine like terms: 5.830951895 + -4 = 1.830951895 x = 1.830951895 Simplifying x = 1.830951895Subproblem 2
x + 4 = -5.830951895 Simplifying x + 4 = -5.830951895 Reorder the terms: 4 + x = -5.830951895 Solving 4 + x = -5.830951895 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -5.830951895 + -4 Combine like terms: 4 + -4 = 0 0 + x = -5.830951895 + -4 x = -5.830951895 + -4 Combine like terms: -5.830951895 + -4 = -9.830951895 x = -9.830951895 Simplifying x = -9.830951895Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.830951895, -9.830951895}
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