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Simplifying (x + 10)(x + -4) = (x + 2) * 2 Reorder the terms: (10 + x)(x + -4) = (x + 2) * 2 Reorder the terms: (10 + x)(-4 + x) = (x + 2) * 2 Multiply (10 + x) * (-4 + x) (10(-4 + x) + x(-4 + x)) = (x + 2) * 2 ((-4 * 10 + x * 10) + x(-4 + x)) = (x + 2) * 2 ((-40 + 10x) + x(-4 + x)) = (x + 2) * 2 (-40 + 10x + (-4 * x + x * x)) = (x + 2) * 2 (-40 + 10x + (-4x + x2)) = (x + 2) * 2 Combine like terms: 10x + -4x = 6x (-40 + 6x + x2) = (x + 2) * 2 Reorder the terms: -40 + 6x + x2 = (2 + x) * 2 Reorder the terms for easier multiplication: -40 + 6x + x2 = 2(2 + x) -40 + 6x + x2 = (2 * 2 + x * 2) -40 + 6x + x2 = (4 + 2x) Solving -40 + 6x + x2 = 4 + 2x Solving for variable 'x'. Reorder the terms: -40 + -4 + 6x + -2x + x2 = 4 + 2x + -4 + -2x Combine like terms: -40 + -4 = -44 -44 + 6x + -2x + x2 = 4 + 2x + -4 + -2x Combine like terms: 6x + -2x = 4x -44 + 4x + x2 = 4 + 2x + -4 + -2x Reorder the terms: -44 + 4x + x2 = 4 + -4 + 2x + -2x Combine like terms: 4 + -4 = 0 -44 + 4x + x2 = 0 + 2x + -2x -44 + 4x + x2 = 2x + -2x Combine like terms: 2x + -2x = 0 -44 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '44' to each side of the equation. -44 + 4x + 44 + x2 = 0 + 44 Reorder the terms: -44 + 44 + 4x + x2 = 0 + 44 Combine like terms: -44 + 44 = 0 0 + 4x + x2 = 0 + 44 4x + x2 = 0 + 44 Combine like terms: 0 + 44 = 44 4x + x2 = 44 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 = 44 + 4 Reorder the terms: 4 + 4x + x2 = 44 + 4 Combine like terms: 44 + 4 = 48 4 + 4x + x2 = 48 Factor a perfect square on the left side: (x + 2)(x + 2) = 48 Calculate the square root of the right side: 6.92820323 Break this problem into two subproblems by setting (x + 2) equal to 6.92820323 and -6.92820323.Subproblem 1
x + 2 = 6.92820323 Simplifying x + 2 = 6.92820323 Reorder the terms: 2 + x = 6.92820323 Solving 2 + x = 6.92820323 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 = 6.92820323 + -2 Combine like terms: 2 + -2 = 0 0 + x = 6.92820323 + -2 x = 6.92820323 + -2 Combine like terms: 6.92820323 + -2 = 4.92820323 x = 4.92820323 Simplifying x = 4.92820323Subproblem 2
x + 2 = -6.92820323 Simplifying x + 2 = -6.92820323 Reorder the terms: 2 + x = -6.92820323 Solving 2 + x = -6.92820323 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 = -6.92820323 + -2 Combine like terms: 2 + -2 = 0 0 + x = -6.92820323 + -2 x = -6.92820323 + -2 Combine like terms: -6.92820323 + -2 = -8.92820323 x = -8.92820323 Simplifying x = -8.92820323Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.92820323, -8.92820323}
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