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Simplifying 12x + -23 + 4(x2 + 4x + 4) = 49 Reorder the terms: 12x + -23 + 4(4 + 4x + x2) = 49 12x + -23 + (4 * 4 + 4x * 4 + x2 * 4) = 49 12x + -23 + (16 + 16x + 4x2) = 49 Reorder the terms: -23 + 16 + 12x + 16x + 4x2 = 49 Combine like terms: -23 + 16 = -7 -7 + 12x + 16x + 4x2 = 49 Combine like terms: 12x + 16x = 28x -7 + 28x + 4x2 = 49 Solving -7 + 28x + 4x2 = 49 Solving for variable 'x'. Reorder the terms: -7 + -49 + 28x + 4x2 = 49 + -49 Combine like terms: -7 + -49 = -56 -56 + 28x + 4x2 = 49 + -49 Combine like terms: 49 + -49 = 0 -56 + 28x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-14 + 7x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-14 + 7x + x2)' equal to zero and attempt to solve: Simplifying -14 + 7x + x2 = 0 Solving -14 + 7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '14' to each side of the equation. -14 + 7x + 14 + x2 = 0 + 14 Reorder the terms: -14 + 14 + 7x + x2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + 7x + x2 = 0 + 14 7x + x2 = 0 + 14 Combine like terms: 0 + 14 = 14 7x + x2 = 14 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = 14 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 14 + 12.25 Combine like terms: 14 + 12.25 = 26.25 12.25 + 7x + x2 = 26.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 26.25 Calculate the square root of the right side: 5.123475383 Break this problem into two subproblems by setting (x + 3.5) equal to 5.123475383 and -5.123475383.Subproblem 1
x + 3.5 = 5.123475383 Simplifying x + 3.5 = 5.123475383 Reorder the terms: 3.5 + x = 5.123475383 Solving 3.5 + x = 5.123475383 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 5.123475383 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 5.123475383 + -3.5 x = 5.123475383 + -3.5 Combine like terms: 5.123475383 + -3.5 = 1.623475383 x = 1.623475383 Simplifying x = 1.623475383Subproblem 2
x + 3.5 = -5.123475383 Simplifying x + 3.5 = -5.123475383 Reorder the terms: 3.5 + x = -5.123475383 Solving 3.5 + x = -5.123475383 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -5.123475383 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -5.123475383 + -3.5 x = -5.123475383 + -3.5 Combine like terms: -5.123475383 + -3.5 = -8.623475383 x = -8.623475383 Simplifying x = -8.623475383Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.623475383, -8.623475383}Solution
x = {1.623475383, -8.623475383}
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