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Simplifying (3x + 2)(3x + 2) + 5 = 2 Reorder the terms: (2 + 3x)(3x + 2) + 5 = 2 Reorder the terms: (2 + 3x)(2 + 3x) + 5 = 2 Multiply (2 + 3x) * (2 + 3x) (2(2 + 3x) + 3x * (2 + 3x)) + 5 = 2 ((2 * 2 + 3x * 2) + 3x * (2 + 3x)) + 5 = 2 ((4 + 6x) + 3x * (2 + 3x)) + 5 = 2 (4 + 6x + (2 * 3x + 3x * 3x)) + 5 = 2 (4 + 6x + (6x + 9x2)) + 5 = 2 Combine like terms: 6x + 6x = 12x (4 + 12x + 9x2) + 5 = 2 Reorder the terms: 4 + 5 + 12x + 9x2 = 2 Combine like terms: 4 + 5 = 9 9 + 12x + 9x2 = 2 Solving 9 + 12x + 9x2 = 2 Solving for variable 'x'. Reorder the terms: 9 + -2 + 12x + 9x2 = 2 + -2 Combine like terms: 9 + -2 = 7 7 + 12x + 9x2 = 2 + -2 Combine like terms: 2 + -2 = 0 7 + 12x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.7777777778 + 1.333333333x + x2 = 0 Move the constant term to the right: Add '-0.7777777778' to each side of the equation. 0.7777777778 + 1.333333333x + -0.7777777778 + x2 = 0 + -0.7777777778 Reorder the terms: 0.7777777778 + -0.7777777778 + 1.333333333x + x2 = 0 + -0.7777777778 Combine like terms: 0.7777777778 + -0.7777777778 = 0.0000000000 0.0000000000 + 1.333333333x + x2 = 0 + -0.7777777778 1.333333333x + x2 = 0 + -0.7777777778 Combine like terms: 0 + -0.7777777778 = -0.7777777778 1.333333333x + x2 = -0.7777777778 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 = -0.7777777778 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333x + x2 = -0.7777777778 + 0.4444444442 Combine like terms: -0.7777777778 + 0.4444444442 = -0.3333333336 0.4444444442 + 1.333333333x + x2 = -0.3333333336 Factor a perfect square on the left side: (x + 0.6666666665)(x + 0.6666666665) = -0.3333333336 Can't calculate square root of the right side. The solution to this equation could not be determined.
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