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Simplifying (x + -2)(x + 2) = 11x + -7 Reorder the terms: (-2 + x)(x + 2) = 11x + -7 Reorder the terms: (-2 + x)(2 + x) = 11x + -7 Multiply (-2 + x) * (2 + x) (-2(2 + x) + x(2 + x)) = 11x + -7 ((2 * -2 + x * -2) + x(2 + x)) = 11x + -7 ((-4 + -2x) + x(2 + x)) = 11x + -7 (-4 + -2x + (2 * x + x * x)) = 11x + -7 (-4 + -2x + (2x + x2)) = 11x + -7 Combine like terms: -2x + 2x = 0 (-4 + 0 + x2) = 11x + -7 (-4 + x2) = 11x + -7 Reorder the terms: -4 + x2 = -7 + 11x Solving -4 + x2 = -7 + 11x Solving for variable 'x'. Reorder the terms: -4 + 7 + -11x + x2 = -7 + 11x + 7 + -11x Combine like terms: -4 + 7 = 3 3 + -11x + x2 = -7 + 11x + 7 + -11x Reorder the terms: 3 + -11x + x2 = -7 + 7 + 11x + -11x Combine like terms: -7 + 7 = 0 3 + -11x + x2 = 0 + 11x + -11x 3 + -11x + x2 = 11x + -11x Combine like terms: 11x + -11x = 0 3 + -11x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + -11x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + -11x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -11x + x2 = 0 + -3 -11x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 -11x + x2 = -3 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 = -3 + 30.25 Reorder the terms: 30.25 + -11x + x2 = -3 + 30.25 Combine like terms: -3 + 30.25 = 27.25 30.25 + -11x + x2 = 27.25 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 27.25 Calculate the square root of the right side: 5.220153254 Break this problem into two subproblems by setting (x + -5.5) equal to 5.220153254 and -5.220153254.Subproblem 1
x + -5.5 = 5.220153254 Simplifying x + -5.5 = 5.220153254 Reorder the terms: -5.5 + x = 5.220153254 Solving -5.5 + x = 5.220153254 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 = 5.220153254 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 5.220153254 + 5.5 x = 5.220153254 + 5.5 Combine like terms: 5.220153254 + 5.5 = 10.720153254 x = 10.720153254 Simplifying x = 10.720153254Subproblem 2
x + -5.5 = -5.220153254 Simplifying x + -5.5 = -5.220153254 Reorder the terms: -5.5 + x = -5.220153254 Solving -5.5 + x = -5.220153254 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 = -5.220153254 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -5.220153254 + 5.5 x = -5.220153254 + 5.5 Combine like terms: -5.220153254 + 5.5 = 0.279846746 x = 0.279846746 Simplifying x = 0.279846746Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.720153254, 0.279846746}
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