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Simplifying 3(4x + 2) = 5 + x(3 + -1x) Reorder the terms: 3(2 + 4x) = 5 + x(3 + -1x) (2 * 3 + 4x * 3) = 5 + x(3 + -1x) (6 + 12x) = 5 + x(3 + -1x) 6 + 12x = 5 + (3 * x + -1x * x) 6 + 12x = 5 + (3x + -1x2) Solving 6 + 12x = 5 + 3x + -1x2 Solving for variable 'x'. Reorder the terms: 6 + -5 + 12x + -3x + x2 = 5 + 3x + -1x2 + -5 + -3x + x2 Combine like terms: 6 + -5 = 1 1 + 12x + -3x + x2 = 5 + 3x + -1x2 + -5 + -3x + x2 Combine like terms: 12x + -3x = 9x 1 + 9x + x2 = 5 + 3x + -1x2 + -5 + -3x + x2 Reorder the terms: 1 + 9x + x2 = 5 + -5 + 3x + -3x + -1x2 + x2 Combine like terms: 5 + -5 = 0 1 + 9x + x2 = 0 + 3x + -3x + -1x2 + x2 1 + 9x + x2 = 3x + -3x + -1x2 + x2 Combine like terms: 3x + -3x = 0 1 + 9x + x2 = 0 + -1x2 + x2 1 + 9x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 1 + 9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + 9x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + 9x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 9x + x2 = 0 + -1 9x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 9x + x2 = -1 The x term is 9x. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9x + 20.25 + x2 = -1 + 20.25 Reorder the terms: 20.25 + 9x + x2 = -1 + 20.25 Combine like terms: -1 + 20.25 = 19.25 20.25 + 9x + x2 = 19.25 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 19.25 Calculate the square root of the right side: 4.387482194 Break this problem into two subproblems by setting (x + 4.5) equal to 4.387482194 and -4.387482194.Subproblem 1
x + 4.5 = 4.387482194 Simplifying x + 4.5 = 4.387482194 Reorder the terms: 4.5 + x = 4.387482194 Solving 4.5 + x = 4.387482194 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = 4.387482194 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 4.387482194 + -4.5 x = 4.387482194 + -4.5 Combine like terms: 4.387482194 + -4.5 = -0.112517806 x = -0.112517806 Simplifying x = -0.112517806Subproblem 2
x + 4.5 = -4.387482194 Simplifying x + 4.5 = -4.387482194 Reorder the terms: 4.5 + x = -4.387482194 Solving 4.5 + x = -4.387482194 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = -4.387482194 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -4.387482194 + -4.5 x = -4.387482194 + -4.5 Combine like terms: -4.387482194 + -4.5 = -8.887482194 x = -8.887482194 Simplifying x = -8.887482194Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.112517806, -8.887482194}
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