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Simplifying (2x + 4)(x + 4) = 196 Reorder the terms: (4 + 2x)(x + 4) = 196 Reorder the terms: (4 + 2x)(4 + x) = 196 Multiply (4 + 2x) * (4 + x) (4(4 + x) + 2x * (4 + x)) = 196 ((4 * 4 + x * 4) + 2x * (4 + x)) = 196 ((16 + 4x) + 2x * (4 + x)) = 196 (16 + 4x + (4 * 2x + x * 2x)) = 196 (16 + 4x + (8x + 2x2)) = 196 Combine like terms: 4x + 8x = 12x (16 + 12x + 2x2) = 196 Solving 16 + 12x + 2x2 = 196 Solving for variable 'x'. Reorder the terms: 16 + -196 + 12x + 2x2 = 196 + -196 Combine like terms: 16 + -196 = -180 -180 + 12x + 2x2 = 196 + -196 Combine like terms: 196 + -196 = 0 -180 + 12x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-90 + 6x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-90 + 6x + x2)' equal to zero and attempt to solve: Simplifying -90 + 6x + x2 = 0 Solving -90 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '90' to each side of the equation. -90 + 6x + 90 + x2 = 0 + 90 Reorder the terms: -90 + 90 + 6x + x2 = 0 + 90 Combine like terms: -90 + 90 = 0 0 + 6x + x2 = 0 + 90 6x + x2 = 0 + 90 Combine like terms: 0 + 90 = 90 6x + x2 = 90 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 90 + 9 Reorder the terms: 9 + 6x + x2 = 90 + 9 Combine like terms: 90 + 9 = 99 9 + 6x + x2 = 99 Factor a perfect square on the left side: (x + 3)(x + 3) = 99 Calculate the square root of the right side: 9.949874371 Break this problem into two subproblems by setting (x + 3) equal to 9.949874371 and -9.949874371.Subproblem 1
x + 3 = 9.949874371 Simplifying x + 3 = 9.949874371 Reorder the terms: 3 + x = 9.949874371 Solving 3 + x = 9.949874371 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 9.949874371 + -3 Combine like terms: 3 + -3 = 0 0 + x = 9.949874371 + -3 x = 9.949874371 + -3 Combine like terms: 9.949874371 + -3 = 6.949874371 x = 6.949874371 Simplifying x = 6.949874371Subproblem 2
x + 3 = -9.949874371 Simplifying x + 3 = -9.949874371 Reorder the terms: 3 + x = -9.949874371 Solving 3 + x = -9.949874371 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -9.949874371 + -3 Combine like terms: 3 + -3 = 0 0 + x = -9.949874371 + -3 x = -9.949874371 + -3 Combine like terms: -9.949874371 + -3 = -12.949874371 x = -12.949874371 Simplifying x = -12.949874371Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.949874371, -12.949874371}Solution
x = {6.949874371, -12.949874371}
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