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Simplifying (x + -4)(x + -7) = 6 Reorder the terms: (-4 + x)(x + -7) = 6 Reorder the terms: (-4 + x)(-7 + x) = 6 Multiply (-4 + x) * (-7 + x) (-4(-7 + x) + x(-7 + x)) = 6 ((-7 * -4 + x * -4) + x(-7 + x)) = 6 ((28 + -4x) + x(-7 + x)) = 6 (28 + -4x + (-7 * x + x * x)) = 6 (28 + -4x + (-7x + x2)) = 6 Combine like terms: -4x + -7x = -11x (28 + -11x + x2) = 6 Solving 28 + -11x + x2 = 6 Solving for variable 'x'. Reorder the terms: 28 + -6 + -11x + x2 = 6 + -6 Combine like terms: 28 + -6 = 22 22 + -11x + x2 = 6 + -6 Combine like terms: 6 + -6 = 0 22 + -11x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-22' to each side of the equation. 22 + -11x + -22 + x2 = 0 + -22 Reorder the terms: 22 + -22 + -11x + x2 = 0 + -22 Combine like terms: 22 + -22 = 0 0 + -11x + x2 = 0 + -22 -11x + x2 = 0 + -22 Combine like terms: 0 + -22 = -22 -11x + x2 = -22 The x term is -11x. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11x + 30.25 + x2 = -22 + 30.25 Reorder the terms: 30.25 + -11x + x2 = -22 + 30.25 Combine like terms: -22 + 30.25 = 8.25 30.25 + -11x + x2 = 8.25 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 8.25 Calculate the square root of the right side: 2.872281323 Break this problem into two subproblems by setting (x + -5.5) equal to 2.872281323 and -2.872281323.Subproblem 1
x + -5.5 = 2.872281323 Simplifying x + -5.5 = 2.872281323 Reorder the terms: -5.5 + x = 2.872281323 Solving -5.5 + x = 2.872281323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = 2.872281323 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 2.872281323 + 5.5 x = 2.872281323 + 5.5 Combine like terms: 2.872281323 + 5.5 = 8.372281323 x = 8.372281323 Simplifying x = 8.372281323Subproblem 2
x + -5.5 = -2.872281323 Simplifying x + -5.5 = -2.872281323 Reorder the terms: -5.5 + x = -2.872281323 Solving -5.5 + x = -2.872281323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = -2.872281323 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -2.872281323 + 5.5 x = -2.872281323 + 5.5 Combine like terms: -2.872281323 + 5.5 = 2.627718677 x = 2.627718677 Simplifying x = 2.627718677Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.372281323, 2.627718677}
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