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Simplifying (x + 5)(4x + 12) = 2 Reorder the terms: (5 + x)(4x + 12) = 2 Reorder the terms: (5 + x)(12 + 4x) = 2 Multiply (5 + x) * (12 + 4x) (5(12 + 4x) + x(12 + 4x)) = 2 ((12 * 5 + 4x * 5) + x(12 + 4x)) = 2 ((60 + 20x) + x(12 + 4x)) = 2 (60 + 20x + (12 * x + 4x * x)) = 2 (60 + 20x + (12x + 4x2)) = 2 Combine like terms: 20x + 12x = 32x (60 + 32x + 4x2) = 2 Solving 60 + 32x + 4x2 = 2 Solving for variable 'x'. Reorder the terms: 60 + -2 + 32x + 4x2 = 2 + -2 Combine like terms: 60 + -2 = 58 58 + 32x + 4x2 = 2 + -2 Combine like terms: 2 + -2 = 0 58 + 32x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(29 + 16x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(29 + 16x + 2x2)' equal to zero and attempt to solve: Simplifying 29 + 16x + 2x2 = 0 Solving 29 + 16x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 14.5 + 8x + x2 = 0 Move the constant term to the right: Add '-14.5' to each side of the equation. 14.5 + 8x + -14.5 + x2 = 0 + -14.5 Reorder the terms: 14.5 + -14.5 + 8x + x2 = 0 + -14.5 Combine like terms: 14.5 + -14.5 = 0.0 0.0 + 8x + x2 = 0 + -14.5 8x + x2 = 0 + -14.5 Combine like terms: 0 + -14.5 = -14.5 8x + x2 = -14.5 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 = -14.5 + 16 Reorder the terms: 16 + 8x + x2 = -14.5 + 16 Combine like terms: -14.5 + 16 = 1.5 16 + 8x + x2 = 1.5 Factor a perfect square on the left side: (x + 4)(x + 4) = 1.5 Calculate the square root of the right side: 1.224744871 Break this problem into two subproblems by setting (x + 4) equal to 1.224744871 and -1.224744871.Subproblem 1
x + 4 = 1.224744871 Simplifying x + 4 = 1.224744871 Reorder the terms: 4 + x = 1.224744871 Solving 4 + x = 1.224744871 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 = 1.224744871 + -4 Combine like terms: 4 + -4 = 0 0 + x = 1.224744871 + -4 x = 1.224744871 + -4 Combine like terms: 1.224744871 + -4 = -2.775255129 x = -2.775255129 Simplifying x = -2.775255129Subproblem 2
x + 4 = -1.224744871 Simplifying x + 4 = -1.224744871 Reorder the terms: 4 + x = -1.224744871 Solving 4 + x = -1.224744871 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 = -1.224744871 + -4 Combine like terms: 4 + -4 = 0 0 + x = -1.224744871 + -4 x = -1.224744871 + -4 Combine like terms: -1.224744871 + -4 = -5.224744871 x = -5.224744871 Simplifying x = -5.224744871Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.775255129, -5.224744871}Solution
x = {-2.775255129, -5.224744871}
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