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Simplifying (x + 3)(x + 3) = 6 + 4(x + 2) Reorder the terms: (3 + x)(x + 3) = 6 + 4(x + 2) Reorder the terms: (3 + x)(3 + x) = 6 + 4(x + 2) Multiply (3 + x) * (3 + x) (3(3 + x) + x(3 + x)) = 6 + 4(x + 2) ((3 * 3 + x * 3) + x(3 + x)) = 6 + 4(x + 2) ((9 + 3x) + x(3 + x)) = 6 + 4(x + 2) (9 + 3x + (3 * x + x * x)) = 6 + 4(x + 2) (9 + 3x + (3x + x2)) = 6 + 4(x + 2) Combine like terms: 3x + 3x = 6x (9 + 6x + x2) = 6 + 4(x + 2) Reorder the terms: 9 + 6x + x2 = 6 + 4(2 + x) 9 + 6x + x2 = 6 + (2 * 4 + x * 4) 9 + 6x + x2 = 6 + (8 + 4x) Combine like terms: 6 + 8 = 14 9 + 6x + x2 = 14 + 4x Solving 9 + 6x + x2 = 14 + 4x Solving for variable 'x'. Reorder the terms: 9 + -14 + 6x + -4x + x2 = 14 + 4x + -14 + -4x Combine like terms: 9 + -14 = -5 -5 + 6x + -4x + x2 = 14 + 4x + -14 + -4x Combine like terms: 6x + -4x = 2x -5 + 2x + x2 = 14 + 4x + -14 + -4x Reorder the terms: -5 + 2x + x2 = 14 + -14 + 4x + -4x Combine like terms: 14 + -14 = 0 -5 + 2x + x2 = 0 + 4x + -4x -5 + 2x + x2 = 4x + -4x Combine like terms: 4x + -4x = 0 -5 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + 2x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + 2x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 2x + x2 = 0 + 5 2x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 2x + x2 = 5 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 5 + 1 Reorder the terms: 1 + 2x + x2 = 5 + 1 Combine like terms: 5 + 1 = 6 1 + 2x + x2 = 6 Factor a perfect square on the left side: (x + 1)(x + 1) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (x + 1) equal to 2.449489743 and -2.449489743.Subproblem 1
x + 1 = 2.449489743 Simplifying x + 1 = 2.449489743 Reorder the terms: 1 + x = 2.449489743 Solving 1 + x = 2.449489743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 2.449489743 + -1 Combine like terms: 1 + -1 = 0 0 + x = 2.449489743 + -1 x = 2.449489743 + -1 Combine like terms: 2.449489743 + -1 = 1.449489743 x = 1.449489743 Simplifying x = 1.449489743Subproblem 2
x + 1 = -2.449489743 Simplifying x + 1 = -2.449489743 Reorder the terms: 1 + x = -2.449489743 Solving 1 + x = -2.449489743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -2.449489743 + -1 Combine like terms: 1 + -1 = 0 0 + x = -2.449489743 + -1 x = -2.449489743 + -1 Combine like terms: -2.449489743 + -1 = -3.449489743 x = -3.449489743 Simplifying x = -3.449489743Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.449489743, -3.449489743}
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