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Simplifying (3x + -2)(3x + -2) = 32 Reorder the terms: (-2 + 3x)(3x + -2) = 32 Reorder the terms: (-2 + 3x)(-2 + 3x) = 32 Multiply (-2 + 3x) * (-2 + 3x) (-2(-2 + 3x) + 3x * (-2 + 3x)) = 32 ((-2 * -2 + 3x * -2) + 3x * (-2 + 3x)) = 32 ((4 + -6x) + 3x * (-2 + 3x)) = 32 (4 + -6x + (-2 * 3x + 3x * 3x)) = 32 (4 + -6x + (-6x + 9x2)) = 32 Combine like terms: -6x + -6x = -12x (4 + -12x + 9x2) = 32 Solving 4 + -12x + 9x2 = 32 Solving for variable 'x'. Reorder the terms: 4 + -32 + -12x + 9x2 = 32 + -32 Combine like terms: 4 + -32 = -28 -28 + -12x + 9x2 = 32 + -32 Combine like terms: 32 + -32 = 0 -28 + -12x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -3.111111111 + -1.333333333x + x2 = 0 Move the constant term to the right: Add '3.111111111' to each side of the equation. -3.111111111 + -1.333333333x + 3.111111111 + x2 = 0 + 3.111111111 Reorder the terms: -3.111111111 + 3.111111111 + -1.333333333x + x2 = 0 + 3.111111111 Combine like terms: -3.111111111 + 3.111111111 = 0.000000000 0.000000000 + -1.333333333x + x2 = 0 + 3.111111111 -1.333333333x + x2 = 0 + 3.111111111 Combine like terms: 0 + 3.111111111 = 3.111111111 -1.333333333x + x2 = 3.111111111 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 = 3.111111111 + 0.4444444442 Reorder the terms: 0.4444444442 + -1.333333333x + x2 = 3.111111111 + 0.4444444442 Combine like terms: 3.111111111 + 0.4444444442 = 3.5555555552 0.4444444442 + -1.333333333x + x2 = 3.5555555552 Factor a perfect square on the left side: (x + -0.6666666665)(x + -0.6666666665) = 3.5555555552 Calculate the square root of the right side: 1.885618083 Break this problem into two subproblems by setting (x + -0.6666666665) equal to 1.885618083 and -1.885618083.Subproblem 1
x + -0.6666666665 = 1.885618083 Simplifying x + -0.6666666665 = 1.885618083 Reorder the terms: -0.6666666665 + x = 1.885618083 Solving -0.6666666665 + x = 1.885618083 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 = 1.885618083 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = 1.885618083 + 0.6666666665 x = 1.885618083 + 0.6666666665 Combine like terms: 1.885618083 + 0.6666666665 = 2.5522847495 x = 2.5522847495 Simplifying x = 2.5522847495Subproblem 2
x + -0.6666666665 = -1.885618083 Simplifying x + -0.6666666665 = -1.885618083 Reorder the terms: -0.6666666665 + x = -1.885618083 Solving -0.6666666665 + x = -1.885618083 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 = -1.885618083 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = -1.885618083 + 0.6666666665 x = -1.885618083 + 0.6666666665 Combine like terms: -1.885618083 + 0.6666666665 = -1.2189514165 x = -1.2189514165 Simplifying x = -1.2189514165Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.5522847495, -1.2189514165}
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