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Simplifying 4x2 + 12x = x2 + -6 Reorder the terms: 12x + 4x2 = x2 + -6 Reorder the terms: 12x + 4x2 = -6 + x2 Solving 12x + 4x2 = -6 + x2 Solving for variable 'x'. Reorder the terms: 6 + 12x + 4x2 + -1x2 = -6 + x2 + 6 + -1x2 Combine like terms: 4x2 + -1x2 = 3x2 6 + 12x + 3x2 = -6 + x2 + 6 + -1x2 Reorder the terms: 6 + 12x + 3x2 = -6 + 6 + x2 + -1x2 Combine like terms: -6 + 6 = 0 6 + 12x + 3x2 = 0 + x2 + -1x2 6 + 12x + 3x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 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 = 2 4 + 4x + x2 = 2 Factor a perfect square on the left side: (x + 2)(x + 2) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (x + 2) equal to 1.414213562 and -1.414213562.Subproblem 1
x + 2 = 1.414213562 Simplifying x + 2 = 1.414213562 Reorder the terms: 2 + x = 1.414213562 Solving 2 + x = 1.414213562 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 = 1.414213562 + -2 Combine like terms: 2 + -2 = 0 0 + x = 1.414213562 + -2 x = 1.414213562 + -2 Combine like terms: 1.414213562 + -2 = -0.585786438 x = -0.585786438 Simplifying x = -0.585786438Subproblem 2
x + 2 = -1.414213562 Simplifying x + 2 = -1.414213562 Reorder the terms: 2 + x = -1.414213562 Solving 2 + x = -1.414213562 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 = -1.414213562 + -2 Combine like terms: 2 + -2 = 0 0 + x = -1.414213562 + -2 x = -1.414213562 + -2 Combine like terms: -1.414213562 + -2 = -3.414213562 x = -3.414213562 Simplifying x = -3.414213562Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.585786438, -3.414213562}Solution
x = {-0.585786438, -3.414213562}
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