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Simplifying 2x(x + 3) + 2x = 46 Reorder the terms: 2x(3 + x) + 2x = 46 (3 * 2x + x * 2x) + 2x = 46 (6x + 2x2) + 2x = 46 Reorder the terms: 6x + 2x + 2x2 = 46 Combine like terms: 6x + 2x = 8x 8x + 2x2 = 46 Solving 8x + 2x2 = 46 Solving for variable 'x'. Reorder the terms: -46 + 8x + 2x2 = 46 + -46 Combine like terms: 46 + -46 = 0 -46 + 8x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-23 + 4x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-23 + 4x + x2)' equal to zero and attempt to solve: Simplifying -23 + 4x + x2 = 0 Solving -23 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '23' to each side of the equation. -23 + 4x + 23 + x2 = 0 + 23 Reorder the terms: -23 + 23 + 4x + x2 = 0 + 23 Combine like terms: -23 + 23 = 0 0 + 4x + x2 = 0 + 23 4x + x2 = 0 + 23 Combine like terms: 0 + 23 = 23 4x + x2 = 23 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 = 23 + 4 Reorder the terms: 4 + 4x + x2 = 23 + 4 Combine like terms: 23 + 4 = 27 4 + 4x + x2 = 27 Factor a perfect square on the left side: (x + 2)(x + 2) = 27 Calculate the square root of the right side: 5.196152423 Break this problem into two subproblems by setting (x + 2) equal to 5.196152423 and -5.196152423.Subproblem 1
x + 2 = 5.196152423 Simplifying x + 2 = 5.196152423 Reorder the terms: 2 + x = 5.196152423 Solving 2 + x = 5.196152423 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 = 5.196152423 + -2 Combine like terms: 2 + -2 = 0 0 + x = 5.196152423 + -2 x = 5.196152423 + -2 Combine like terms: 5.196152423 + -2 = 3.196152423 x = 3.196152423 Simplifying x = 3.196152423Subproblem 2
x + 2 = -5.196152423 Simplifying x + 2 = -5.196152423 Reorder the terms: 2 + x = -5.196152423 Solving 2 + x = -5.196152423 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 = -5.196152423 + -2 Combine like terms: 2 + -2 = 0 0 + x = -5.196152423 + -2 x = -5.196152423 + -2 Combine like terms: -5.196152423 + -2 = -7.196152423 x = -7.196152423 Simplifying x = -7.196152423Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.196152423, -7.196152423}Solution
x = {3.196152423, -7.196152423}
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