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Simplifying (x + 2)(x + -7) = 9 Reorder the terms: (2 + x)(x + -7) = 9 Reorder the terms: (2 + x)(-7 + x) = 9 Multiply (2 + x) * (-7 + x) (2(-7 + x) + x(-7 + x)) = 9 ((-7 * 2 + x * 2) + x(-7 + x)) = 9 ((-14 + 2x) + x(-7 + x)) = 9 (-14 + 2x + (-7 * x + x * x)) = 9 (-14 + 2x + (-7x + x2)) = 9 Combine like terms: 2x + -7x = -5x (-14 + -5x + x2) = 9 Solving -14 + -5x + x2 = 9 Solving for variable 'x'. Reorder the terms: -14 + -9 + -5x + x2 = 9 + -9 Combine like terms: -14 + -9 = -23 -23 + -5x + x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -23 + -5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '23' to each side of the equation. -23 + -5x + 23 + x2 = 0 + 23 Reorder the terms: -23 + 23 + -5x + x2 = 0 + 23 Combine like terms: -23 + 23 = 0 0 + -5x + x2 = 0 + 23 -5x + x2 = 0 + 23 Combine like terms: 0 + 23 = 23 -5x + x2 = 23 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 = 23 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 23 + 6.25 Combine like terms: 23 + 6.25 = 29.25 6.25 + -5x + x2 = 29.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 29.25 Calculate the square root of the right side: 5.408326913 Break this problem into two subproblems by setting (x + -2.5) equal to 5.408326913 and -5.408326913.Subproblem 1
x + -2.5 = 5.408326913 Simplifying x + -2.5 = 5.408326913 Reorder the terms: -2.5 + x = 5.408326913 Solving -2.5 + x = 5.408326913 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 = 5.408326913 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 5.408326913 + 2.5 x = 5.408326913 + 2.5 Combine like terms: 5.408326913 + 2.5 = 7.908326913 x = 7.908326913 Simplifying x = 7.908326913Subproblem 2
x + -2.5 = -5.408326913 Simplifying x + -2.5 = -5.408326913 Reorder the terms: -2.5 + x = -5.408326913 Solving -2.5 + x = -5.408326913 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 = -5.408326913 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -5.408326913 + 2.5 x = -5.408326913 + 2.5 Combine like terms: -5.408326913 + 2.5 = -2.908326913 x = -2.908326913 Simplifying x = -2.908326913Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.908326913, -2.908326913}
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