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Simplifying (x + 9)(x + -4) = 138 Reorder the terms: (9 + x)(x + -4) = 138 Reorder the terms: (9 + x)(-4 + x) = 138 Multiply (9 + x) * (-4 + x) (9(-4 + x) + x(-4 + x)) = 138 ((-4 * 9 + x * 9) + x(-4 + x)) = 138 ((-36 + 9x) + x(-4 + x)) = 138 (-36 + 9x + (-4 * x + x * x)) = 138 (-36 + 9x + (-4x + x2)) = 138 Combine like terms: 9x + -4x = 5x (-36 + 5x + x2) = 138 Solving -36 + 5x + x2 = 138 Solving for variable 'x'. Reorder the terms: -36 + -138 + 5x + x2 = 138 + -138 Combine like terms: -36 + -138 = -174 -174 + 5x + x2 = 138 + -138 Combine like terms: 138 + -138 = 0 -174 + 5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '174' to each side of the equation. -174 + 5x + 174 + x2 = 0 + 174 Reorder the terms: -174 + 174 + 5x + x2 = 0 + 174 Combine like terms: -174 + 174 = 0 0 + 5x + x2 = 0 + 174 5x + x2 = 0 + 174 Combine like terms: 0 + 174 = 174 5x + x2 = 174 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 = 174 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 174 + 6.25 Combine like terms: 174 + 6.25 = 180.25 6.25 + 5x + x2 = 180.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 180.25 Calculate the square root of the right side: 13.425721582 Break this problem into two subproblems by setting (x + 2.5) equal to 13.425721582 and -13.425721582.Subproblem 1
x + 2.5 = 13.425721582 Simplifying x + 2.5 = 13.425721582 Reorder the terms: 2.5 + x = 13.425721582 Solving 2.5 + x = 13.425721582 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 = 13.425721582 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 13.425721582 + -2.5 x = 13.425721582 + -2.5 Combine like terms: 13.425721582 + -2.5 = 10.925721582 x = 10.925721582 Simplifying x = 10.925721582Subproblem 2
x + 2.5 = -13.425721582 Simplifying x + 2.5 = -13.425721582 Reorder the terms: 2.5 + x = -13.425721582 Solving 2.5 + x = -13.425721582 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 = -13.425721582 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -13.425721582 + -2.5 x = -13.425721582 + -2.5 Combine like terms: -13.425721582 + -2.5 = -15.925721582 x = -15.925721582 Simplifying x = -15.925721582Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.925721582, -15.925721582}
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