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Simplifying (x + -4)(x + -4) + -6 = 0 Reorder the terms: (-4 + x)(x + -4) + -6 = 0 Reorder the terms: (-4 + x)(-4 + x) + -6 = 0 Multiply (-4 + x) * (-4 + x) (-4(-4 + x) + x(-4 + x)) + -6 = 0 ((-4 * -4 + x * -4) + x(-4 + x)) + -6 = 0 ((16 + -4x) + x(-4 + x)) + -6 = 0 (16 + -4x + (-4 * x + x * x)) + -6 = 0 (16 + -4x + (-4x + x2)) + -6 = 0 Combine like terms: -4x + -4x = -8x (16 + -8x + x2) + -6 = 0 Reorder the terms: 16 + -6 + -8x + x2 = 0 Combine like terms: 16 + -6 = 10 10 + -8x + x2 = 0 Solving 10 + -8x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-10' to each side of the equation. 10 + -8x + -10 + x2 = 0 + -10 Reorder the terms: 10 + -10 + -8x + x2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -8x + x2 = 0 + -10 -8x + x2 = 0 + -10 Combine like terms: 0 + -10 = -10 -8x + x2 = -10 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 = -10 + 16 Reorder the terms: 16 + -8x + x2 = -10 + 16 Combine like terms: -10 + 16 = 6 16 + -8x + x2 = 6 Factor a perfect square on the left side: (x + -4)(x + -4) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (x + -4) equal to 2.449489743 and -2.449489743.Subproblem 1
x + -4 = 2.449489743 Simplifying x + -4 = 2.449489743 Reorder the terms: -4 + x = 2.449489743 Solving -4 + x = 2.449489743 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 = 2.449489743 + 4 Combine like terms: -4 + 4 = 0 0 + x = 2.449489743 + 4 x = 2.449489743 + 4 Combine like terms: 2.449489743 + 4 = 6.449489743 x = 6.449489743 Simplifying x = 6.449489743Subproblem 2
x + -4 = -2.449489743 Simplifying x + -4 = -2.449489743 Reorder the terms: -4 + x = -2.449489743 Solving -4 + x = -2.449489743 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 = -2.449489743 + 4 Combine like terms: -4 + 4 = 0 0 + x = -2.449489743 + 4 x = -2.449489743 + 4 Combine like terms: -2.449489743 + 4 = 1.550510257 x = 1.550510257 Simplifying x = 1.550510257Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.449489743, 1.550510257}
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