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Simplifying (x + 2)(x + 2) = 117 Reorder the terms: (2 + x)(x + 2) = 117 Reorder the terms: (2 + x)(2 + x) = 117 Multiply (2 + x) * (2 + x) (2(2 + x) + x(2 + x)) = 117 ((2 * 2 + x * 2) + x(2 + x)) = 117 ((4 + 2x) + x(2 + x)) = 117 (4 + 2x + (2 * x + x * x)) = 117 (4 + 2x + (2x + x2)) = 117 Combine like terms: 2x + 2x = 4x (4 + 4x + x2) = 117 Solving 4 + 4x + x2 = 117 Solving for variable 'x'. Reorder the terms: 4 + -117 + 4x + x2 = 117 + -117 Combine like terms: 4 + -117 = -113 -113 + 4x + x2 = 117 + -117 Combine like terms: 117 + -117 = 0 -113 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '113' to each side of the equation. -113 + 4x + 113 + x2 = 0 + 113 Reorder the terms: -113 + 113 + 4x + x2 = 0 + 113 Combine like terms: -113 + 113 = 0 0 + 4x + x2 = 0 + 113 4x + x2 = 0 + 113 Combine like terms: 0 + 113 = 113 4x + x2 = 113 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 113 + 4 Reorder the terms: 4 + 4x + x2 = 113 + 4 Combine like terms: 113 + 4 = 117 4 + 4x + x2 = 117 Factor a perfect square on the left side: (x + 2)(x + 2) = 117 Calculate the square root of the right side: 10.816653826 Break this problem into two subproblems by setting (x + 2) equal to 10.816653826 and -10.816653826.Subproblem 1
x + 2 = 10.816653826 Simplifying x + 2 = 10.816653826 Reorder the terms: 2 + x = 10.816653826 Solving 2 + x = 10.816653826 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 10.816653826 + -2 Combine like terms: 2 + -2 = 0 0 + x = 10.816653826 + -2 x = 10.816653826 + -2 Combine like terms: 10.816653826 + -2 = 8.816653826 x = 8.816653826 Simplifying x = 8.816653826Subproblem 2
x + 2 = -10.816653826 Simplifying x + 2 = -10.816653826 Reorder the terms: 2 + x = -10.816653826 Solving 2 + x = -10.816653826 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -10.816653826 + -2 Combine like terms: 2 + -2 = 0 0 + x = -10.816653826 + -2 x = -10.816653826 + -2 Combine like terms: -10.816653826 + -2 = -12.816653826 x = -12.816653826 Simplifying x = -12.816653826Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.816653826, -12.816653826}
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