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Simplifying (x + 6)(x + -2) = 7 Reorder the terms: (6 + x)(x + -2) = 7 Reorder the terms: (6 + x)(-2 + x) = 7 Multiply (6 + x) * (-2 + x) (6(-2 + x) + x(-2 + x)) = 7 ((-2 * 6 + x * 6) + x(-2 + x)) = 7 ((-12 + 6x) + x(-2 + x)) = 7 (-12 + 6x + (-2 * x + x * x)) = 7 (-12 + 6x + (-2x + x2)) = 7 Combine like terms: 6x + -2x = 4x (-12 + 4x + x2) = 7 Solving -12 + 4x + x2 = 7 Solving for variable 'x'. Reorder the terms: -12 + -7 + 4x + x2 = 7 + -7 Combine like terms: -12 + -7 = -19 -19 + 4x + x2 = 7 + -7 Combine like terms: 7 + -7 = 0 -19 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '19' to each side of the equation. -19 + 4x + 19 + x2 = 0 + 19 Reorder the terms: -19 + 19 + 4x + x2 = 0 + 19 Combine like terms: -19 + 19 = 0 0 + 4x + x2 = 0 + 19 4x + x2 = 0 + 19 Combine like terms: 0 + 19 = 19 4x + x2 = 19 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 = 19 + 4 Reorder the terms: 4 + 4x + x2 = 19 + 4 Combine like terms: 19 + 4 = 23 4 + 4x + x2 = 23 Factor a perfect square on the left side: (x + 2)(x + 2) = 23 Calculate the square root of the right side: 4.795831523 Break this problem into two subproblems by setting (x + 2) equal to 4.795831523 and -4.795831523.Subproblem 1
x + 2 = 4.795831523 Simplifying x + 2 = 4.795831523 Reorder the terms: 2 + x = 4.795831523 Solving 2 + x = 4.795831523 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 = 4.795831523 + -2 Combine like terms: 2 + -2 = 0 0 + x = 4.795831523 + -2 x = 4.795831523 + -2 Combine like terms: 4.795831523 + -2 = 2.795831523 x = 2.795831523 Simplifying x = 2.795831523Subproblem 2
x + 2 = -4.795831523 Simplifying x + 2 = -4.795831523 Reorder the terms: 2 + x = -4.795831523 Solving 2 + x = -4.795831523 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 = -4.795831523 + -2 Combine like terms: 2 + -2 = 0 0 + x = -4.795831523 + -2 x = -4.795831523 + -2 Combine like terms: -4.795831523 + -2 = -6.795831523 x = -6.795831523 Simplifying x = -6.795831523Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.795831523, -6.795831523}
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