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Simplifying ((x + 2)(x + 2)) + -4 = 3 Reorder the terms: ((2 + x)(x + 2)) + -4 = 3 Reorder the terms: ((2 + x)(2 + x)) + -4 = 3 Multiply (2 + x) * (2 + x) ((2(2 + x) + x(2 + x))) + -4 = 3 (((2 * 2 + x * 2) + x(2 + x))) + -4 = 3 (((4 + 2x) + x(2 + x))) + -4 = 3 ((4 + 2x + (2 * x + x * x))) + -4 = 3 ((4 + 2x + (2x + x2))) + -4 = 3 Combine like terms: 2x + 2x = 4x ((4 + 4x + x2)) + -4 = 3 (4 + 4x + x2) + -4 = 3 Remove parenthesis around (4 + 4x + x2) 4 + 4x + x2 + -4 = 3 Reorder the terms: 4 + -4 + 4x + x2 = 3 Combine like terms: 4 + -4 = 0 0 + 4x + x2 = 3 4x + x2 = 3 Solving 4x + x2 = 3 Solving for variable 'x'. Reorder the terms: -3 + 4x + x2 = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + 4x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + 4x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 4x + x2 = 0 + 3 4x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 4x + x2 = 3 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 = 3 + 4 Reorder the terms: 4 + 4x + x2 = 3 + 4 Combine like terms: 3 + 4 = 7 4 + 4x + x2 = 7 Factor a perfect square on the left side: (x + 2)(x + 2) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (x + 2) equal to 2.645751311 and -2.645751311.Subproblem 1
x + 2 = 2.645751311 Simplifying x + 2 = 2.645751311 Reorder the terms: 2 + x = 2.645751311 Solving 2 + x = 2.645751311 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 = 2.645751311 + -2 Combine like terms: 2 + -2 = 0 0 + x = 2.645751311 + -2 x = 2.645751311 + -2 Combine like terms: 2.645751311 + -2 = 0.645751311 x = 0.645751311 Simplifying x = 0.645751311Subproblem 2
x + 2 = -2.645751311 Simplifying x + 2 = -2.645751311 Reorder the terms: 2 + x = -2.645751311 Solving 2 + x = -2.645751311 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 = -2.645751311 + -2 Combine like terms: 2 + -2 = 0 0 + x = -2.645751311 + -2 x = -2.645751311 + -2 Combine like terms: -2.645751311 + -2 = -4.645751311 x = -4.645751311 Simplifying x = -4.645751311Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.645751311, -4.645751311}
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