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Simplifying (x + -2)(x + -3) = 9x + 11 Reorder the terms: (-2 + x)(x + -3) = 9x + 11 Reorder the terms: (-2 + x)(-3 + x) = 9x + 11 Multiply (-2 + x) * (-3 + x) (-2(-3 + x) + x(-3 + x)) = 9x + 11 ((-3 * -2 + x * -2) + x(-3 + x)) = 9x + 11 ((6 + -2x) + x(-3 + x)) = 9x + 11 (6 + -2x + (-3 * x + x * x)) = 9x + 11 (6 + -2x + (-3x + x2)) = 9x + 11 Combine like terms: -2x + -3x = -5x (6 + -5x + x2) = 9x + 11 Reorder the terms: 6 + -5x + x2 = 11 + 9x Solving 6 + -5x + x2 = 11 + 9x Solving for variable 'x'. Reorder the terms: 6 + -11 + -5x + -9x + x2 = 11 + 9x + -11 + -9x Combine like terms: 6 + -11 = -5 -5 + -5x + -9x + x2 = 11 + 9x + -11 + -9x Combine like terms: -5x + -9x = -14x -5 + -14x + x2 = 11 + 9x + -11 + -9x Reorder the terms: -5 + -14x + x2 = 11 + -11 + 9x + -9x Combine like terms: 11 + -11 = 0 -5 + -14x + x2 = 0 + 9x + -9x -5 + -14x + x2 = 9x + -9x Combine like terms: 9x + -9x = 0 -5 + -14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + -14x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + -14x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -14x + x2 = 0 + 5 -14x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 -14x + x2 = 5 The x term is -14x. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14x + 49 + x2 = 5 + 49 Reorder the terms: 49 + -14x + x2 = 5 + 49 Combine like terms: 5 + 49 = 54 49 + -14x + x2 = 54 Factor a perfect square on the left side: (x + -7)(x + -7) = 54 Calculate the square root of the right side: 7.348469228 Break this problem into two subproblems by setting (x + -7) equal to 7.348469228 and -7.348469228.Subproblem 1
x + -7 = 7.348469228 Simplifying x + -7 = 7.348469228 Reorder the terms: -7 + x = 7.348469228 Solving -7 + x = 7.348469228 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = 7.348469228 + 7 Combine like terms: -7 + 7 = 0 0 + x = 7.348469228 + 7 x = 7.348469228 + 7 Combine like terms: 7.348469228 + 7 = 14.348469228 x = 14.348469228 Simplifying x = 14.348469228Subproblem 2
x + -7 = -7.348469228 Simplifying x + -7 = -7.348469228 Reorder the terms: -7 + x = -7.348469228 Solving -7 + x = -7.348469228 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = -7.348469228 + 7 Combine like terms: -7 + 7 = 0 0 + x = -7.348469228 + 7 x = -7.348469228 + 7 Combine like terms: -7.348469228 + 7 = -0.348469228 x = -0.348469228 Simplifying x = -0.348469228Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.348469228, -0.348469228}
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