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Simplifying (3 + x)(x + -8) = 8 Reorder the terms: (3 + x)(-8 + x) = 8 Multiply (3 + x) * (-8 + x) (3(-8 + x) + x(-8 + x)) = 8 ((-8 * 3 + x * 3) + x(-8 + x)) = 8 ((-24 + 3x) + x(-8 + x)) = 8 (-24 + 3x + (-8 * x + x * x)) = 8 (-24 + 3x + (-8x + x2)) = 8 Combine like terms: 3x + -8x = -5x (-24 + -5x + x2) = 8 Solving -24 + -5x + x2 = 8 Solving for variable 'x'. Reorder the terms: -24 + -8 + -5x + x2 = 8 + -8 Combine like terms: -24 + -8 = -32 -32 + -5x + x2 = 8 + -8 Combine like terms: 8 + -8 = 0 -32 + -5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '32' to each side of the equation. -32 + -5x + 32 + x2 = 0 + 32 Reorder the terms: -32 + 32 + -5x + x2 = 0 + 32 Combine like terms: -32 + 32 = 0 0 + -5x + x2 = 0 + 32 -5x + x2 = 0 + 32 Combine like terms: 0 + 32 = 32 -5x + x2 = 32 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 32 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 32 + 6.25 Combine like terms: 32 + 6.25 = 38.25 6.25 + -5x + x2 = 38.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 38.25 Calculate the square root of the right side: 6.184658438 Break this problem into two subproblems by setting (x + -2.5) equal to 6.184658438 and -6.184658438.Subproblem 1
x + -2.5 = 6.184658438 Simplifying x + -2.5 = 6.184658438 Reorder the terms: -2.5 + x = 6.184658438 Solving -2.5 + x = 6.184658438 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 6.184658438 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 6.184658438 + 2.5 x = 6.184658438 + 2.5 Combine like terms: 6.184658438 + 2.5 = 8.684658438 x = 8.684658438 Simplifying x = 8.684658438Subproblem 2
x + -2.5 = -6.184658438 Simplifying x + -2.5 = -6.184658438 Reorder the terms: -2.5 + x = -6.184658438 Solving -2.5 + x = -6.184658438 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -6.184658438 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -6.184658438 + 2.5 x = -6.184658438 + 2.5 Combine like terms: -6.184658438 + 2.5 = -3.684658438 x = -3.684658438 Simplifying x = -3.684658438Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.684658438, -3.684658438}
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