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Simplifying (x + -4)(x + -6) = 11 Reorder the terms: (-4 + x)(x + -6) = 11 Reorder the terms: (-4 + x)(-6 + x) = 11 Multiply (-4 + x) * (-6 + x) (-4(-6 + x) + x(-6 + x)) = 11 ((-6 * -4 + x * -4) + x(-6 + x)) = 11 ((24 + -4x) + x(-6 + x)) = 11 (24 + -4x + (-6 * x + x * x)) = 11 (24 + -4x + (-6x + x2)) = 11 Combine like terms: -4x + -6x = -10x (24 + -10x + x2) = 11 Solving 24 + -10x + x2 = 11 Solving for variable 'x'. Reorder the terms: 24 + -11 + -10x + x2 = 11 + -11 Combine like terms: 24 + -11 = 13 13 + -10x + x2 = 11 + -11 Combine like terms: 11 + -11 = 0 13 + -10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-13' to each side of the equation. 13 + -10x + -13 + x2 = 0 + -13 Reorder the terms: 13 + -13 + -10x + x2 = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -10x + x2 = 0 + -13 -10x + x2 = 0 + -13 Combine like terms: 0 + -13 = -13 -10x + x2 = -13 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = -13 + 25 Reorder the terms: 25 + -10x + x2 = -13 + 25 Combine like terms: -13 + 25 = 12 25 + -10x + x2 = 12 Factor a perfect square on the left side: (x + -5)(x + -5) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (x + -5) equal to 3.464101615 and -3.464101615.Subproblem 1
x + -5 = 3.464101615 Simplifying x + -5 = 3.464101615 Reorder the terms: -5 + x = 3.464101615 Solving -5 + x = 3.464101615 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 3.464101615 + 5 Combine like terms: -5 + 5 = 0 0 + x = 3.464101615 + 5 x = 3.464101615 + 5 Combine like terms: 3.464101615 + 5 = 8.464101615 x = 8.464101615 Simplifying x = 8.464101615Subproblem 2
x + -5 = -3.464101615 Simplifying x + -5 = -3.464101615 Reorder the terms: -5 + x = -3.464101615 Solving -5 + x = -3.464101615 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -3.464101615 + 5 Combine like terms: -5 + 5 = 0 0 + x = -3.464101615 + 5 x = -3.464101615 + 5 Combine like terms: -3.464101615 + 5 = 1.535898385 x = 1.535898385 Simplifying x = 1.535898385Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.464101615, 1.535898385}
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