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Simplifying (x + 8)(x + -2) = (x + 2) * 2 Reorder the terms: (8 + x)(x + -2) = (x + 2) * 2 Reorder the terms: (8 + x)(-2 + x) = (x + 2) * 2 Multiply (8 + x) * (-2 + x) (8(-2 + x) + x(-2 + x)) = (x + 2) * 2 ((-2 * 8 + x * 8) + x(-2 + x)) = (x + 2) * 2 ((-16 + 8x) + x(-2 + x)) = (x + 2) * 2 (-16 + 8x + (-2 * x + x * x)) = (x + 2) * 2 (-16 + 8x + (-2x + x2)) = (x + 2) * 2 Combine like terms: 8x + -2x = 6x (-16 + 6x + x2) = (x + 2) * 2 Reorder the terms: -16 + 6x + x2 = (2 + x) * 2 Reorder the terms for easier multiplication: -16 + 6x + x2 = 2(2 + x) -16 + 6x + x2 = (2 * 2 + x * 2) -16 + 6x + x2 = (4 + 2x) Solving -16 + 6x + x2 = 4 + 2x Solving for variable 'x'. Reorder the terms: -16 + -4 + 6x + -2x + x2 = 4 + 2x + -4 + -2x Combine like terms: -16 + -4 = -20 -20 + 6x + -2x + x2 = 4 + 2x + -4 + -2x Combine like terms: 6x + -2x = 4x -20 + 4x + x2 = 4 + 2x + -4 + -2x Reorder the terms: -20 + 4x + x2 = 4 + -4 + 2x + -2x Combine like terms: 4 + -4 = 0 -20 + 4x + x2 = 0 + 2x + -2x -20 + 4x + x2 = 2x + -2x Combine like terms: 2x + -2x = 0 -20 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '20' to each side of the equation. -20 + 4x + 20 + x2 = 0 + 20 Reorder the terms: -20 + 20 + 4x + x2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + 4x + x2 = 0 + 20 4x + x2 = 0 + 20 Combine like terms: 0 + 20 = 20 4x + x2 = 20 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 = 20 + 4 Reorder the terms: 4 + 4x + x2 = 20 + 4 Combine like terms: 20 + 4 = 24 4 + 4x + x2 = 24 Factor a perfect square on the left side: (x + 2)(x + 2) = 24 Calculate the square root of the right side: 4.898979486 Break this problem into two subproblems by setting (x + 2) equal to 4.898979486 and -4.898979486.Subproblem 1
x + 2 = 4.898979486 Simplifying x + 2 = 4.898979486 Reorder the terms: 2 + x = 4.898979486 Solving 2 + x = 4.898979486 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 = 4.898979486 + -2 Combine like terms: 2 + -2 = 0 0 + x = 4.898979486 + -2 x = 4.898979486 + -2 Combine like terms: 4.898979486 + -2 = 2.898979486 x = 2.898979486 Simplifying x = 2.898979486Subproblem 2
x + 2 = -4.898979486 Simplifying x + 2 = -4.898979486 Reorder the terms: 2 + x = -4.898979486 Solving 2 + x = -4.898979486 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 = -4.898979486 + -2 Combine like terms: 2 + -2 = 0 0 + x = -4.898979486 + -2 x = -4.898979486 + -2 Combine like terms: -4.898979486 + -2 = -6.898979486 x = -6.898979486 Simplifying x = -6.898979486Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.898979486, -6.898979486}
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