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Simplifying (x + -5)(x + 8) = 10 Reorder the terms: (-5 + x)(x + 8) = 10 Reorder the terms: (-5 + x)(8 + x) = 10 Multiply (-5 + x) * (8 + x) (-5(8 + x) + x(8 + x)) = 10 ((8 * -5 + x * -5) + x(8 + x)) = 10 ((-40 + -5x) + x(8 + x)) = 10 (-40 + -5x + (8 * x + x * x)) = 10 (-40 + -5x + (8x + x2)) = 10 Combine like terms: -5x + 8x = 3x (-40 + 3x + x2) = 10 Solving -40 + 3x + x2 = 10 Solving for variable 'x'. Reorder the terms: -40 + -10 + 3x + x2 = 10 + -10 Combine like terms: -40 + -10 = -50 -50 + 3x + x2 = 10 + -10 Combine like terms: 10 + -10 = 0 -50 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '50' to each side of the equation. -50 + 3x + 50 + x2 = 0 + 50 Reorder the terms: -50 + 50 + 3x + x2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + 3x + x2 = 0 + 50 3x + x2 = 0 + 50 Combine like terms: 0 + 50 = 50 3x + x2 = 50 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 = 50 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 50 + 2.25 Combine like terms: 50 + 2.25 = 52.25 2.25 + 3x + x2 = 52.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 52.25 Calculate the square root of the right side: 7.228416147 Break this problem into two subproblems by setting (x + 1.5) equal to 7.228416147 and -7.228416147.Subproblem 1
x + 1.5 = 7.228416147 Simplifying x + 1.5 = 7.228416147 Reorder the terms: 1.5 + x = 7.228416147 Solving 1.5 + x = 7.228416147 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 = 7.228416147 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 7.228416147 + -1.5 x = 7.228416147 + -1.5 Combine like terms: 7.228416147 + -1.5 = 5.728416147 x = 5.728416147 Simplifying x = 5.728416147Subproblem 2
x + 1.5 = -7.228416147 Simplifying x + 1.5 = -7.228416147 Reorder the terms: 1.5 + x = -7.228416147 Solving 1.5 + x = -7.228416147 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 = -7.228416147 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -7.228416147 + -1.5 x = -7.228416147 + -1.5 Combine like terms: -7.228416147 + -1.5 = -8.728416147 x = -8.728416147 Simplifying x = -8.728416147Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.728416147, -8.728416147}
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