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Simplifying (x + -3)(x + 4) = 6 Reorder the terms: (-3 + x)(x + 4) = 6 Reorder the terms: (-3 + x)(4 + x) = 6 Multiply (-3 + x) * (4 + x) (-3(4 + x) + x(4 + x)) = 6 ((4 * -3 + x * -3) + x(4 + x)) = 6 ((-12 + -3x) + x(4 + x)) = 6 (-12 + -3x + (4 * x + x * x)) = 6 (-12 + -3x + (4x + x2)) = 6 Combine like terms: -3x + 4x = 1x (-12 + 1x + x2) = 6 Solving -12 + 1x + x2 = 6 Solving for variable 'x'. Reorder the terms: -12 + -6 + 1x + x2 = 6 + -6 Combine like terms: -12 + -6 = -18 -18 + 1x + x2 = 6 + -6 Combine like terms: 6 + -6 = 0 -18 + 1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '18' to each side of the equation. -18 + 1x + 18 + x2 = 0 + 18 Reorder the terms: -18 + 18 + 1x + x2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + 1x + x2 = 0 + 18 1x + x2 = 0 + 18 Combine like terms: 0 + 18 = 18 1x + x2 = 18 The x term is 1x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. x + 0.25 + x2 = 18 + 0.25 Reorder the terms: 0.25 + x + x2 = 18 + 0.25 Combine like terms: 18 + 0.25 = 18.25 0.25 + x + x2 = 18.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 18.25 Calculate the square root of the right side: 4.272001873 Break this problem into two subproblems by setting (x + 0.5) equal to 4.272001873 and -4.272001873.Subproblem 1
x + 0.5 = 4.272001873 Simplifying x + 0.5 = 4.272001873 Reorder the terms: 0.5 + x = 4.272001873 Solving 0.5 + x = 4.272001873 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 4.272001873 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 4.272001873 + -0.5 x = 4.272001873 + -0.5 Combine like terms: 4.272001873 + -0.5 = 3.772001873 x = 3.772001873 Simplifying x = 3.772001873Subproblem 2
x + 0.5 = -4.272001873 Simplifying x + 0.5 = -4.272001873 Reorder the terms: 0.5 + x = -4.272001873 Solving 0.5 + x = -4.272001873 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -4.272001873 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -4.272001873 + -0.5 x = -4.272001873 + -0.5 Combine like terms: -4.272001873 + -0.5 = -4.772001873 x = -4.772001873 Simplifying x = -4.772001873Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.772001873, -4.772001873}
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