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Simplifying (2x + 1)(4x + 4) = 18 Reorder the terms: (1 + 2x)(4x + 4) = 18 Reorder the terms: (1 + 2x)(4 + 4x) = 18 Multiply (1 + 2x) * (4 + 4x) (1(4 + 4x) + 2x * (4 + 4x)) = 18 ((4 * 1 + 4x * 1) + 2x * (4 + 4x)) = 18 ((4 + 4x) + 2x * (4 + 4x)) = 18 (4 + 4x + (4 * 2x + 4x * 2x)) = 18 (4 + 4x + (8x + 8x2)) = 18 Combine like terms: 4x + 8x = 12x (4 + 12x + 8x2) = 18 Solving 4 + 12x + 8x2 = 18 Solving for variable 'x'. Reorder the terms: 4 + -18 + 12x + 8x2 = 18 + -18 Combine like terms: 4 + -18 = -14 -14 + 12x + 8x2 = 18 + -18 Combine like terms: 18 + -18 = 0 -14 + 12x + 8x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-7 + 6x + 4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-7 + 6x + 4x2)' equal to zero and attempt to solve: Simplifying -7 + 6x + 4x2 = 0 Solving -7 + 6x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.75 + 1.5x + x2 = 0 Move the constant term to the right: Add '1.75' to each side of the equation. -1.75 + 1.5x + 1.75 + x2 = 0 + 1.75 Reorder the terms: -1.75 + 1.75 + 1.5x + x2 = 0 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + 1.5x + x2 = 0 + 1.75 1.5x + x2 = 0 + 1.75 Combine like terms: 0 + 1.75 = 1.75 1.5x + x2 = 1.75 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = 1.75 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 1.75 + 0.5625 Combine like terms: 1.75 + 0.5625 = 2.3125 0.5625 + 1.5x + x2 = 2.3125 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 2.3125 Calculate the square root of the right side: 1.520690633 Break this problem into two subproblems by setting (x + 0.75) equal to 1.520690633 and -1.520690633.Subproblem 1
x + 0.75 = 1.520690633 Simplifying x + 0.75 = 1.520690633 Reorder the terms: 0.75 + x = 1.520690633 Solving 0.75 + x = 1.520690633 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 1.520690633 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 1.520690633 + -0.75 x = 1.520690633 + -0.75 Combine like terms: 1.520690633 + -0.75 = 0.770690633 x = 0.770690633 Simplifying x = 0.770690633Subproblem 2
x + 0.75 = -1.520690633 Simplifying x + 0.75 = -1.520690633 Reorder the terms: 0.75 + x = -1.520690633 Solving 0.75 + x = -1.520690633 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -1.520690633 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -1.520690633 + -0.75 x = -1.520690633 + -0.75 Combine like terms: -1.520690633 + -0.75 = -2.270690633 x = -2.270690633 Simplifying x = -2.270690633Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.770690633, -2.270690633}Solution
x = {0.770690633, -2.270690633}
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