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Simplifying (4 + -9x)(3x + 2) = 5x Reorder the terms: (4 + -9x)(2 + 3x) = 5x Multiply (4 + -9x) * (2 + 3x) (4(2 + 3x) + -9x * (2 + 3x)) = 5x ((2 * 4 + 3x * 4) + -9x * (2 + 3x)) = 5x ((8 + 12x) + -9x * (2 + 3x)) = 5x (8 + 12x + (2 * -9x + 3x * -9x)) = 5x (8 + 12x + (-18x + -27x2)) = 5x Combine like terms: 12x + -18x = -6x (8 + -6x + -27x2) = 5x Solving 8 + -6x + -27x2 = 5x Solving for variable 'x'. Reorder the terms: 8 + -6x + -5x + -27x2 = 5x + -5x Combine like terms: -6x + -5x = -11x 8 + -11x + -27x2 = 5x + -5x Combine like terms: 5x + -5x = 0 8 + -11x + -27x2 = 0 Begin completing the square. Divide all terms by -27 the coefficient of the squared term: Divide each side by '-27'. -0.2962962963 + 0.4074074074x + x2 = 0 Move the constant term to the right: Add '0.2962962963' to each side of the equation. -0.2962962963 + 0.4074074074x + 0.2962962963 + x2 = 0 + 0.2962962963 Reorder the terms: -0.2962962963 + 0.2962962963 + 0.4074074074x + x2 = 0 + 0.2962962963 Combine like terms: -0.2962962963 + 0.2962962963 = 0.0000000000 0.0000000000 + 0.4074074074x + x2 = 0 + 0.2962962963 0.4074074074x + x2 = 0 + 0.2962962963 Combine like terms: 0 + 0.2962962963 = 0.2962962963 0.4074074074x + x2 = 0.2962962963 The x term is 0.4074074074x. Take half its coefficient (0.2037037037). Square it (0.04149519890) and add it to both sides. Add '0.04149519890' to each side of the equation. 0.4074074074x + 0.04149519890 + x2 = 0.2962962963 + 0.04149519890 Reorder the terms: 0.04149519890 + 0.4074074074x + x2 = 0.2962962963 + 0.04149519890 Combine like terms: 0.2962962963 + 0.04149519890 = 0.3377914952 0.04149519890 + 0.4074074074x + x2 = 0.3377914952 Factor a perfect square on the left side: (x + 0.2037037037)(x + 0.2037037037) = 0.3377914952 Calculate the square root of the right side: 0.581198327 Break this problem into two subproblems by setting (x + 0.2037037037) equal to 0.581198327 and -0.581198327.Subproblem 1
x + 0.2037037037 = 0.581198327 Simplifying x + 0.2037037037 = 0.581198327 Reorder the terms: 0.2037037037 + x = 0.581198327 Solving 0.2037037037 + x = 0.581198327 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2037037037' to each side of the equation. 0.2037037037 + -0.2037037037 + x = 0.581198327 + -0.2037037037 Combine like terms: 0.2037037037 + -0.2037037037 = 0.0000000000 0.0000000000 + x = 0.581198327 + -0.2037037037 x = 0.581198327 + -0.2037037037 Combine like terms: 0.581198327 + -0.2037037037 = 0.3774946233 x = 0.3774946233 Simplifying x = 0.3774946233Subproblem 2
x + 0.2037037037 = -0.581198327 Simplifying x + 0.2037037037 = -0.581198327 Reorder the terms: 0.2037037037 + x = -0.581198327 Solving 0.2037037037 + x = -0.581198327 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2037037037' to each side of the equation. 0.2037037037 + -0.2037037037 + x = -0.581198327 + -0.2037037037 Combine like terms: 0.2037037037 + -0.2037037037 = 0.0000000000 0.0000000000 + x = -0.581198327 + -0.2037037037 x = -0.581198327 + -0.2037037037 Combine like terms: -0.581198327 + -0.2037037037 = -0.7849020307 x = -0.7849020307 Simplifying x = -0.7849020307Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.3774946233, -0.7849020307}
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