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Simplifying (x + 8)(x + -5) = 9 Reorder the terms: (8 + x)(x + -5) = 9 Reorder the terms: (8 + x)(-5 + x) = 9 Multiply (8 + x) * (-5 + x) (8(-5 + x) + x(-5 + x)) = 9 ((-5 * 8 + x * 8) + x(-5 + x)) = 9 ((-40 + 8x) + x(-5 + x)) = 9 (-40 + 8x + (-5 * x + x * x)) = 9 (-40 + 8x + (-5x + x2)) = 9 Combine like terms: 8x + -5x = 3x (-40 + 3x + x2) = 9 Solving -40 + 3x + x2 = 9 Solving for variable 'x'. Reorder the terms: -40 + -9 + 3x + x2 = 9 + -9 Combine like terms: -40 + -9 = -49 -49 + 3x + x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -49 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '49' to each side of the equation. -49 + 3x + 49 + x2 = 0 + 49 Reorder the terms: -49 + 49 + 3x + x2 = 0 + 49 Combine like terms: -49 + 49 = 0 0 + 3x + x2 = 0 + 49 3x + x2 = 0 + 49 Combine like terms: 0 + 49 = 49 3x + x2 = 49 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 = 49 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 49 + 2.25 Combine like terms: 49 + 2.25 = 51.25 2.25 + 3x + x2 = 51.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 51.25 Calculate the square root of the right side: 7.158910532 Break this problem into two subproblems by setting (x + 1.5) equal to 7.158910532 and -7.158910532.Subproblem 1
x + 1.5 = 7.158910532 Simplifying x + 1.5 = 7.158910532 Reorder the terms: 1.5 + x = 7.158910532 Solving 1.5 + x = 7.158910532 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 = 7.158910532 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 7.158910532 + -1.5 x = 7.158910532 + -1.5 Combine like terms: 7.158910532 + -1.5 = 5.658910532 x = 5.658910532 Simplifying x = 5.658910532Subproblem 2
x + 1.5 = -7.158910532 Simplifying x + 1.5 = -7.158910532 Reorder the terms: 1.5 + x = -7.158910532 Solving 1.5 + x = -7.158910532 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 = -7.158910532 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -7.158910532 + -1.5 x = -7.158910532 + -1.5 Combine like terms: -7.158910532 + -1.5 = -8.658910532 x = -8.658910532 Simplifying x = -8.658910532Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.658910532, -8.658910532}
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