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Simplifying (2x + 3)(2x + 3) = x * x + 81 Reorder the terms: (3 + 2x)(2x + 3) = x * x + 81 Reorder the terms: (3 + 2x)(3 + 2x) = x * x + 81 Multiply (3 + 2x) * (3 + 2x) (3(3 + 2x) + 2x * (3 + 2x)) = x * x + 81 ((3 * 3 + 2x * 3) + 2x * (3 + 2x)) = x * x + 81 ((9 + 6x) + 2x * (3 + 2x)) = x * x + 81 (9 + 6x + (3 * 2x + 2x * 2x)) = x * x + 81 (9 + 6x + (6x + 4x2)) = x * x + 81 Combine like terms: 6x + 6x = 12x (9 + 12x + 4x2) = x * x + 81 Multiply x * x 9 + 12x + 4x2 = x2 + 81 Reorder the terms: 9 + 12x + 4x2 = 81 + x2 Solving 9 + 12x + 4x2 = 81 + x2 Solving for variable 'x'. Reorder the terms: 9 + -81 + 12x + 4x2 + -1x2 = 81 + x2 + -81 + -1x2 Combine like terms: 9 + -81 = -72 -72 + 12x + 4x2 + -1x2 = 81 + x2 + -81 + -1x2 Combine like terms: 4x2 + -1x2 = 3x2 -72 + 12x + 3x2 = 81 + x2 + -81 + -1x2 Reorder the terms: -72 + 12x + 3x2 = 81 + -81 + x2 + -1x2 Combine like terms: 81 + -81 = 0 -72 + 12x + 3x2 = 0 + x2 + -1x2 -72 + 12x + 3x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -72 + 12x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-24 + 4x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-24 + 4x + x2)' equal to zero and attempt to solve: Simplifying -24 + 4x + x2 = 0 Solving -24 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '24' to each side of the equation. -24 + 4x + 24 + x2 = 0 + 24 Reorder the terms: -24 + 24 + 4x + x2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + 4x + x2 = 0 + 24 4x + x2 = 0 + 24 Combine like terms: 0 + 24 = 24 4x + x2 = 24 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 = 24 + 4 Reorder the terms: 4 + 4x + x2 = 24 + 4 Combine like terms: 24 + 4 = 28 4 + 4x + x2 = 28 Factor a perfect square on the left side: (x + 2)(x + 2) = 28 Calculate the square root of the right side: 5.291502622 Break this problem into two subproblems by setting (x + 2) equal to 5.291502622 and -5.291502622.Subproblem 1
x + 2 = 5.291502622 Simplifying x + 2 = 5.291502622 Reorder the terms: 2 + x = 5.291502622 Solving 2 + x = 5.291502622 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 = 5.291502622 + -2 Combine like terms: 2 + -2 = 0 0 + x = 5.291502622 + -2 x = 5.291502622 + -2 Combine like terms: 5.291502622 + -2 = 3.291502622 x = 3.291502622 Simplifying x = 3.291502622Subproblem 2
x + 2 = -5.291502622 Simplifying x + 2 = -5.291502622 Reorder the terms: 2 + x = -5.291502622 Solving 2 + x = -5.291502622 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 = -5.291502622 + -2 Combine like terms: 2 + -2 = 0 0 + x = -5.291502622 + -2 x = -5.291502622 + -2 Combine like terms: -5.291502622 + -2 = -7.291502622 x = -7.291502622 Simplifying x = -7.291502622Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.291502622, -7.291502622}Solution
x = {3.291502622, -7.291502622}
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