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Simplifying (x + 8)(x + -6) = 24 Reorder the terms: (8 + x)(x + -6) = 24 Reorder the terms: (8 + x)(-6 + x) = 24 Multiply (8 + x) * (-6 + x) (8(-6 + x) + x(-6 + x)) = 24 ((-6 * 8 + x * 8) + x(-6 + x)) = 24 ((-48 + 8x) + x(-6 + x)) = 24 (-48 + 8x + (-6 * x + x * x)) = 24 (-48 + 8x + (-6x + x2)) = 24 Combine like terms: 8x + -6x = 2x (-48 + 2x + x2) = 24 Solving -48 + 2x + x2 = 24 Solving for variable 'x'. Reorder the terms: -48 + -24 + 2x + x2 = 24 + -24 Combine like terms: -48 + -24 = -72 -72 + 2x + x2 = 24 + -24 Combine like terms: 24 + -24 = 0 -72 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '72' to each side of the equation. -72 + 2x + 72 + x2 = 0 + 72 Reorder the terms: -72 + 72 + 2x + x2 = 0 + 72 Combine like terms: -72 + 72 = 0 0 + 2x + x2 = 0 + 72 2x + x2 = 0 + 72 Combine like terms: 0 + 72 = 72 2x + x2 = 72 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 72 + 1 Reorder the terms: 1 + 2x + x2 = 72 + 1 Combine like terms: 72 + 1 = 73 1 + 2x + x2 = 73 Factor a perfect square on the left side: (x + 1)(x + 1) = 73 Calculate the square root of the right side: 8.544003745 Break this problem into two subproblems by setting (x + 1) equal to 8.544003745 and -8.544003745.Subproblem 1
x + 1 = 8.544003745 Simplifying x + 1 = 8.544003745 Reorder the terms: 1 + x = 8.544003745 Solving 1 + x = 8.544003745 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 8.544003745 + -1 Combine like terms: 1 + -1 = 0 0 + x = 8.544003745 + -1 x = 8.544003745 + -1 Combine like terms: 8.544003745 + -1 = 7.544003745 x = 7.544003745 Simplifying x = 7.544003745Subproblem 2
x + 1 = -8.544003745 Simplifying x + 1 = -8.544003745 Reorder the terms: 1 + x = -8.544003745 Solving 1 + x = -8.544003745 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -8.544003745 + -1 Combine like terms: 1 + -1 = 0 0 + x = -8.544003745 + -1 x = -8.544003745 + -1 Combine like terms: -8.544003745 + -1 = -9.544003745 x = -9.544003745 Simplifying x = -9.544003745Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.544003745, -9.544003745}
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