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Simplifying (4x + -1)(2x + 3) = 9x Reorder the terms: (-1 + 4x)(2x + 3) = 9x Reorder the terms: (-1 + 4x)(3 + 2x) = 9x Multiply (-1 + 4x) * (3 + 2x) (-1(3 + 2x) + 4x * (3 + 2x)) = 9x ((3 * -1 + 2x * -1) + 4x * (3 + 2x)) = 9x ((-3 + -2x) + 4x * (3 + 2x)) = 9x (-3 + -2x + (3 * 4x + 2x * 4x)) = 9x (-3 + -2x + (12x + 8x2)) = 9x Combine like terms: -2x + 12x = 10x (-3 + 10x + 8x2) = 9x Solving -3 + 10x + 8x2 = 9x Solving for variable 'x'. Reorder the terms: -3 + 10x + -9x + 8x2 = 9x + -9x Combine like terms: 10x + -9x = 1x -3 + 1x + 8x2 = 9x + -9x Combine like terms: 9x + -9x = 0 -3 + 1x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.375 + 0.125x + x2 = 0 Move the constant term to the right: Add '0.375' to each side of the equation. -0.375 + 0.125x + 0.375 + x2 = 0 + 0.375 Reorder the terms: -0.375 + 0.375 + 0.125x + x2 = 0 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + 0.125x + x2 = 0 + 0.375 0.125x + x2 = 0 + 0.375 Combine like terms: 0 + 0.375 = 0.375 0.125x + x2 = 0.375 The x term is 0.125x. Take half its coefficient (0.0625). Square it (0.00390625) and add it to both sides. Add '0.00390625' to each side of the equation. 0.125x + 0.00390625 + x2 = 0.375 + 0.00390625 Reorder the terms: 0.00390625 + 0.125x + x2 = 0.375 + 0.00390625 Combine like terms: 0.375 + 0.00390625 = 0.37890625 0.00390625 + 0.125x + x2 = 0.37890625 Factor a perfect square on the left side: (x + 0.0625)(x + 0.0625) = 0.37890625 Calculate the square root of the right side: 0.615553613 Break this problem into two subproblems by setting (x + 0.0625) equal to 0.615553613 and -0.615553613.Subproblem 1
x + 0.0625 = 0.615553613 Simplifying x + 0.0625 = 0.615553613 Reorder the terms: 0.0625 + x = 0.615553613 Solving 0.0625 + x = 0.615553613 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0625' to each side of the equation. 0.0625 + -0.0625 + x = 0.615553613 + -0.0625 Combine like terms: 0.0625 + -0.0625 = 0.0000 0.0000 + x = 0.615553613 + -0.0625 x = 0.615553613 + -0.0625 Combine like terms: 0.615553613 + -0.0625 = 0.553053613 x = 0.553053613 Simplifying x = 0.553053613Subproblem 2
x + 0.0625 = -0.615553613 Simplifying x + 0.0625 = -0.615553613 Reorder the terms: 0.0625 + x = -0.615553613 Solving 0.0625 + x = -0.615553613 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0625' to each side of the equation. 0.0625 + -0.0625 + x = -0.615553613 + -0.0625 Combine like terms: 0.0625 + -0.0625 = 0.0000 0.0000 + x = -0.615553613 + -0.0625 x = -0.615553613 + -0.0625 Combine like terms: -0.615553613 + -0.0625 = -0.678053613 x = -0.678053613 Simplifying x = -0.678053613Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.553053613, -0.678053613}
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