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Simplifying x2 = 4x + 4 + 100 Reorder the terms: x2 = 4 + 100 + 4x Combine like terms: 4 + 100 = 104 x2 = 104 + 4x Solving x2 = 104 + 4x Solving for variable 'x'. Reorder the terms: -104 + -4x + x2 = 104 + 4x + -104 + -4x Reorder the terms: -104 + -4x + x2 = 104 + -104 + 4x + -4x Combine like terms: 104 + -104 = 0 -104 + -4x + x2 = 0 + 4x + -4x -104 + -4x + x2 = 4x + -4x Combine like terms: 4x + -4x = 0 -104 + -4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '104' to each side of the equation. -104 + -4x + 104 + x2 = 0 + 104 Reorder the terms: -104 + 104 + -4x + x2 = 0 + 104 Combine like terms: -104 + 104 = 0 0 + -4x + x2 = 0 + 104 -4x + x2 = 0 + 104 Combine like terms: 0 + 104 = 104 -4x + x2 = 104 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 = 104 + 4 Reorder the terms: 4 + -4x + x2 = 104 + 4 Combine like terms: 104 + 4 = 108 4 + -4x + x2 = 108 Factor a perfect square on the left side: (x + -2)(x + -2) = 108 Calculate the square root of the right side: 10.392304845 Break this problem into two subproblems by setting (x + -2) equal to 10.392304845 and -10.392304845.Subproblem 1
x + -2 = 10.392304845 Simplifying x + -2 = 10.392304845 Reorder the terms: -2 + x = 10.392304845 Solving -2 + x = 10.392304845 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 = 10.392304845 + 2 Combine like terms: -2 + 2 = 0 0 + x = 10.392304845 + 2 x = 10.392304845 + 2 Combine like terms: 10.392304845 + 2 = 12.392304845 x = 12.392304845 Simplifying x = 12.392304845Subproblem 2
x + -2 = -10.392304845 Simplifying x + -2 = -10.392304845 Reorder the terms: -2 + x = -10.392304845 Solving -2 + x = -10.392304845 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 = -10.392304845 + 2 Combine like terms: -2 + 2 = 0 0 + x = -10.392304845 + 2 x = -10.392304845 + 2 Combine like terms: -10.392304845 + 2 = -8.392304845 x = -8.392304845 Simplifying x = -8.392304845Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.392304845, -8.392304845}
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