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Simplifying (3x + 4) * 2 = 3x(3x + 6) Reorder the terms: (4 + 3x) * 2 = 3x(3x + 6) Reorder the terms for easier multiplication: 2(4 + 3x) = 3x(3x + 6) (4 * 2 + 3x * 2) = 3x(3x + 6) (8 + 6x) = 3x(3x + 6) Reorder the terms: 8 + 6x = 3x(6 + 3x) 8 + 6x = (6 * 3x + 3x * 3x) 8 + 6x = (18x + 9x2) Solving 8 + 6x = 18x + 9x2 Solving for variable 'x'. Combine like terms: 6x + -18x = -12x 8 + -12x + -9x2 = 18x + 9x2 + -18x + -9x2 Reorder the terms: 8 + -12x + -9x2 = 18x + -18x + 9x2 + -9x2 Combine like terms: 18x + -18x = 0 8 + -12x + -9x2 = 0 + 9x2 + -9x2 8 + -12x + -9x2 = 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 8 + -12x + -9x2 = 0 Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. -0.8888888889 + 1.333333333x + x2 = 0 Move the constant term to the right: Add '0.8888888889' to each side of the equation. -0.8888888889 + 1.333333333x + 0.8888888889 + x2 = 0 + 0.8888888889 Reorder the terms: -0.8888888889 + 0.8888888889 + 1.333333333x + x2 = 0 + 0.8888888889 Combine like terms: -0.8888888889 + 0.8888888889 = 0.0000000000 0.0000000000 + 1.333333333x + x2 = 0 + 0.8888888889 1.333333333x + x2 = 0 + 0.8888888889 Combine like terms: 0 + 0.8888888889 = 0.8888888889 1.333333333x + x2 = 0.8888888889 The x term is 1.333333333x. Take half its coefficient (0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. 1.333333333x + 0.4444444442 + x2 = 0.8888888889 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333x + x2 = 0.8888888889 + 0.4444444442 Combine like terms: 0.8888888889 + 0.4444444442 = 1.3333333331 0.4444444442 + 1.333333333x + x2 = 1.3333333331 Factor a perfect square on the left side: (x + 0.6666666665)(x + 0.6666666665) = 1.3333333331 Calculate the square root of the right side: 1.154700538 Break this problem into two subproblems by setting (x + 0.6666666665) equal to 1.154700538 and -1.154700538.Subproblem 1
x + 0.6666666665 = 1.154700538 Simplifying x + 0.6666666665 = 1.154700538 Reorder the terms: 0.6666666665 + x = 1.154700538 Solving 0.6666666665 + x = 1.154700538 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + x = 1.154700538 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = 1.154700538 + -0.6666666665 x = 1.154700538 + -0.6666666665 Combine like terms: 1.154700538 + -0.6666666665 = 0.4880338715 x = 0.4880338715 Simplifying x = 0.4880338715Subproblem 2
x + 0.6666666665 = -1.154700538 Simplifying x + 0.6666666665 = -1.154700538 Reorder the terms: 0.6666666665 + x = -1.154700538 Solving 0.6666666665 + x = -1.154700538 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + x = -1.154700538 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = -1.154700538 + -0.6666666665 x = -1.154700538 + -0.6666666665 Combine like terms: -1.154700538 + -0.6666666665 = -1.8213672045 x = -1.8213672045 Simplifying x = -1.8213672045Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.4880338715, -1.8213672045}
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