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Simplifying 3x(x + 4) = 123 Reorder the terms: 3x(4 + x) = 123 (4 * 3x + x * 3x) = 123 (12x + 3x2) = 123 Solving 12x + 3x2 = 123 Solving for variable 'x'. Reorder the terms: -123 + 12x + 3x2 = 123 + -123 Combine like terms: 123 + -123 = 0 -123 + 12x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-41 + 4x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-41 + 4x + x2)' equal to zero and attempt to solve: Simplifying -41 + 4x + x2 = 0 Solving -41 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '41' to each side of the equation. -41 + 4x + 41 + x2 = 0 + 41 Reorder the terms: -41 + 41 + 4x + x2 = 0 + 41 Combine like terms: -41 + 41 = 0 0 + 4x + x2 = 0 + 41 4x + x2 = 0 + 41 Combine like terms: 0 + 41 = 41 4x + x2 = 41 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 = 41 + 4 Reorder the terms: 4 + 4x + x2 = 41 + 4 Combine like terms: 41 + 4 = 45 4 + 4x + x2 = 45 Factor a perfect square on the left side: (x + 2)(x + 2) = 45 Calculate the square root of the right side: 6.708203933 Break this problem into two subproblems by setting (x + 2) equal to 6.708203933 and -6.708203933.Subproblem 1
x + 2 = 6.708203933 Simplifying x + 2 = 6.708203933 Reorder the terms: 2 + x = 6.708203933 Solving 2 + x = 6.708203933 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 = 6.708203933 + -2 Combine like terms: 2 + -2 = 0 0 + x = 6.708203933 + -2 x = 6.708203933 + -2 Combine like terms: 6.708203933 + -2 = 4.708203933 x = 4.708203933 Simplifying x = 4.708203933Subproblem 2
x + 2 = -6.708203933 Simplifying x + 2 = -6.708203933 Reorder the terms: 2 + x = -6.708203933 Solving 2 + x = -6.708203933 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 = -6.708203933 + -2 Combine like terms: 2 + -2 = 0 0 + x = -6.708203933 + -2 x = -6.708203933 + -2 Combine like terms: -6.708203933 + -2 = -8.708203933 x = -8.708203933 Simplifying x = -8.708203933Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.708203933, -8.708203933}Solution
x = {4.708203933, -8.708203933}
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