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Simplifying (x + 6)(x + -2) = 22 Reorder the terms: (6 + x)(x + -2) = 22 Reorder the terms: (6 + x)(-2 + x) = 22 Multiply (6 + x) * (-2 + x) (6(-2 + x) + x(-2 + x)) = 22 ((-2 * 6 + x * 6) + x(-2 + x)) = 22 ((-12 + 6x) + x(-2 + x)) = 22 (-12 + 6x + (-2 * x + x * x)) = 22 (-12 + 6x + (-2x + x2)) = 22 Combine like terms: 6x + -2x = 4x (-12 + 4x + x2) = 22 Solving -12 + 4x + x2 = 22 Solving for variable 'x'. Reorder the terms: -12 + -22 + 4x + x2 = 22 + -22 Combine like terms: -12 + -22 = -34 -34 + 4x + x2 = 22 + -22 Combine like terms: 22 + -22 = 0 -34 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '34' to each side of the equation. -34 + 4x + 34 + x2 = 0 + 34 Reorder the terms: -34 + 34 + 4x + x2 = 0 + 34 Combine like terms: -34 + 34 = 0 0 + 4x + x2 = 0 + 34 4x + x2 = 0 + 34 Combine like terms: 0 + 34 = 34 4x + x2 = 34 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 34 + 4 Reorder the terms: 4 + 4x + x2 = 34 + 4 Combine like terms: 34 + 4 = 38 4 + 4x + x2 = 38 Factor a perfect square on the left side: (x + 2)(x + 2) = 38 Calculate the square root of the right side: 6.164414003 Break this problem into two subproblems by setting (x + 2) equal to 6.164414003 and -6.164414003.Subproblem 1
x + 2 = 6.164414003 Simplifying x + 2 = 6.164414003 Reorder the terms: 2 + x = 6.164414003 Solving 2 + x = 6.164414003 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 6.164414003 + -2 Combine like terms: 2 + -2 = 0 0 + x = 6.164414003 + -2 x = 6.164414003 + -2 Combine like terms: 6.164414003 + -2 = 4.164414003 x = 4.164414003 Simplifying x = 4.164414003Subproblem 2
x + 2 = -6.164414003 Simplifying x + 2 = -6.164414003 Reorder the terms: 2 + x = -6.164414003 Solving 2 + x = -6.164414003 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -6.164414003 + -2 Combine like terms: 2 + -2 = 0 0 + x = -6.164414003 + -2 x = -6.164414003 + -2 Combine like terms: -6.164414003 + -2 = -8.164414003 x = -8.164414003 Simplifying x = -8.164414003Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.164414003, -8.164414003}
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