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Simplifying 3x2 + 24x + 54 = 12 Reorder the terms: 54 + 24x + 3x2 = 12 Solving 54 + 24x + 3x2 = 12 Solving for variable 'x'. Reorder the terms: 54 + -12 + 24x + 3x2 = 12 + -12 Combine like terms: 54 + -12 = 42 42 + 24x + 3x2 = 12 + -12 Combine like terms: 12 + -12 = 0 42 + 24x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(14 + 8x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(14 + 8x + x2)' equal to zero and attempt to solve: Simplifying 14 + 8x + x2 = 0 Solving 14 + 8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-14' to each side of the equation. 14 + 8x + -14 + x2 = 0 + -14 Reorder the terms: 14 + -14 + 8x + x2 = 0 + -14 Combine like terms: 14 + -14 = 0 0 + 8x + x2 = 0 + -14 8x + x2 = 0 + -14 Combine like terms: 0 + -14 = -14 8x + x2 = -14 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = -14 + 16 Reorder the terms: 16 + 8x + x2 = -14 + 16 Combine like terms: -14 + 16 = 2 16 + 8x + x2 = 2 Factor a perfect square on the left side: (x + 4)(x + 4) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (x + 4) equal to 1.414213562 and -1.414213562.Subproblem 1
x + 4 = 1.414213562 Simplifying x + 4 = 1.414213562 Reorder the terms: 4 + x = 1.414213562 Solving 4 + x = 1.414213562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 1.414213562 + -4 Combine like terms: 4 + -4 = 0 0 + x = 1.414213562 + -4 x = 1.414213562 + -4 Combine like terms: 1.414213562 + -4 = -2.585786438 x = -2.585786438 Simplifying x = -2.585786438Subproblem 2
x + 4 = -1.414213562 Simplifying x + 4 = -1.414213562 Reorder the terms: 4 + x = -1.414213562 Solving 4 + x = -1.414213562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -1.414213562 + -4 Combine like terms: 4 + -4 = 0 0 + x = -1.414213562 + -4 x = -1.414213562 + -4 Combine like terms: -1.414213562 + -4 = -5.414213562 x = -5.414213562 Simplifying x = -5.414213562Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.585786438, -5.414213562}Solution
x = {-2.585786438, -5.414213562}
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