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Simplifying (x + 5)(x + -8) = 3 Reorder the terms: (5 + x)(x + -8) = 3 Reorder the terms: (5 + x)(-8 + x) = 3 Multiply (5 + x) * (-8 + x) (5(-8 + x) + x(-8 + x)) = 3 ((-8 * 5 + x * 5) + x(-8 + x)) = 3 ((-40 + 5x) + x(-8 + x)) = 3 (-40 + 5x + (-8 * x + x * x)) = 3 (-40 + 5x + (-8x + x2)) = 3 Combine like terms: 5x + -8x = -3x (-40 + -3x + x2) = 3 Solving -40 + -3x + x2 = 3 Solving for variable 'x'. Reorder the terms: -40 + -3 + -3x + x2 = 3 + -3 Combine like terms: -40 + -3 = -43 -43 + -3x + x2 = 3 + -3 Combine like terms: 3 + -3 = 0 -43 + -3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '43' to each side of the equation. -43 + -3x + 43 + x2 = 0 + 43 Reorder the terms: -43 + 43 + -3x + x2 = 0 + 43 Combine like terms: -43 + 43 = 0 0 + -3x + x2 = 0 + 43 -3x + x2 = 0 + 43 Combine like terms: 0 + 43 = 43 -3x + x2 = 43 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 43 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 43 + 2.25 Combine like terms: 43 + 2.25 = 45.25 2.25 + -3x + x2 = 45.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 45.25 Calculate the square root of the right side: 6.726812024 Break this problem into two subproblems by setting (x + -1.5) equal to 6.726812024 and -6.726812024.Subproblem 1
x + -1.5 = 6.726812024 Simplifying x + -1.5 = 6.726812024 Reorder the terms: -1.5 + x = 6.726812024 Solving -1.5 + x = 6.726812024 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 6.726812024 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 6.726812024 + 1.5 x = 6.726812024 + 1.5 Combine like terms: 6.726812024 + 1.5 = 8.226812024 x = 8.226812024 Simplifying x = 8.226812024Subproblem 2
x + -1.5 = -6.726812024 Simplifying x + -1.5 = -6.726812024 Reorder the terms: -1.5 + x = -6.726812024 Solving -1.5 + x = -6.726812024 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -6.726812024 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -6.726812024 + 1.5 x = -6.726812024 + 1.5 Combine like terms: -6.726812024 + 1.5 = -5.226812024 x = -5.226812024 Simplifying x = -5.226812024Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.226812024, -5.226812024}
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