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Simplifying 3(x + 2)(x + 2) = 18 Reorder the terms: 3(2 + x)(x + 2) = 18 Reorder the terms: 3(2 + x)(2 + x) = 18 Multiply (2 + x) * (2 + x) 3(2(2 + x) + x(2 + x)) = 18 3((2 * 2 + x * 2) + x(2 + x)) = 18 3((4 + 2x) + x(2 + x)) = 18 3(4 + 2x + (2 * x + x * x)) = 18 3(4 + 2x + (2x + x2)) = 18 Combine like terms: 2x + 2x = 4x 3(4 + 4x + x2) = 18 (4 * 3 + 4x * 3 + x2 * 3) = 18 (12 + 12x + 3x2) = 18 Solving 12 + 12x + 3x2 = 18 Solving for variable 'x'. Reorder the terms: 12 + -18 + 12x + 3x2 = 18 + -18 Combine like terms: 12 + -18 = -6 -6 + 12x + 3x2 = 18 + -18 Combine like terms: 18 + -18 = 0 -6 + 12x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-2 + 4x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-2 + 4x + x2)' equal to zero and attempt to solve: Simplifying -2 + 4x + x2 = 0 Solving -2 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + 4x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + 4x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 4x + x2 = 0 + 2 4x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 4x + x2 = 2 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 = 2 + 4 Reorder the terms: 4 + 4x + x2 = 2 + 4 Combine like terms: 2 + 4 = 6 4 + 4x + x2 = 6 Factor a perfect square on the left side: (x + 2)(x + 2) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (x + 2) equal to 2.449489743 and -2.449489743.Subproblem 1
x + 2 = 2.449489743 Simplifying x + 2 = 2.449489743 Reorder the terms: 2 + x = 2.449489743 Solving 2 + x = 2.449489743 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 = 2.449489743 + -2 Combine like terms: 2 + -2 = 0 0 + x = 2.449489743 + -2 x = 2.449489743 + -2 Combine like terms: 2.449489743 + -2 = 0.449489743 x = 0.449489743 Simplifying x = 0.449489743Subproblem 2
x + 2 = -2.449489743 Simplifying x + 2 = -2.449489743 Reorder the terms: 2 + x = -2.449489743 Solving 2 + x = -2.449489743 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 = -2.449489743 + -2 Combine like terms: 2 + -2 = 0 0 + x = -2.449489743 + -2 x = -2.449489743 + -2 Combine like terms: -2.449489743 + -2 = -4.449489743 x = -4.449489743 Simplifying x = -4.449489743Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.449489743, -4.449489743}Solution
x = {0.449489743, -4.449489743}
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