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Simplifying 4(3x + 2)(3x + 2) = 5 Reorder the terms: 4(2 + 3x)(3x + 2) = 5 Reorder the terms: 4(2 + 3x)(2 + 3x) = 5 Multiply (2 + 3x) * (2 + 3x) 4(2(2 + 3x) + 3x * (2 + 3x)) = 5 4((2 * 2 + 3x * 2) + 3x * (2 + 3x)) = 5 4((4 + 6x) + 3x * (2 + 3x)) = 5 4(4 + 6x + (2 * 3x + 3x * 3x)) = 5 4(4 + 6x + (6x + 9x2)) = 5 Combine like terms: 6x + 6x = 12x 4(4 + 12x + 9x2) = 5 (4 * 4 + 12x * 4 + 9x2 * 4) = 5 (16 + 48x + 36x2) = 5 Solving 16 + 48x + 36x2 = 5 Solving for variable 'x'. Reorder the terms: 16 + -5 + 48x + 36x2 = 5 + -5 Combine like terms: 16 + -5 = 11 11 + 48x + 36x2 = 5 + -5 Combine like terms: 5 + -5 = 0 11 + 48x + 36x2 = 0 Begin completing the square. Divide all terms by 36 the coefficient of the squared term: Divide each side by '36'. 0.3055555556 + 1.333333333x + x2 = 0 Move the constant term to the right: Add '-0.3055555556' to each side of the equation. 0.3055555556 + 1.333333333x + -0.3055555556 + x2 = 0 + -0.3055555556 Reorder the terms: 0.3055555556 + -0.3055555556 + 1.333333333x + x2 = 0 + -0.3055555556 Combine like terms: 0.3055555556 + -0.3055555556 = 0.0000000000 0.0000000000 + 1.333333333x + x2 = 0 + -0.3055555556 1.333333333x + x2 = 0 + -0.3055555556 Combine like terms: 0 + -0.3055555556 = -0.3055555556 1.333333333x + x2 = -0.3055555556 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 = -0.3055555556 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333x + x2 = -0.3055555556 + 0.4444444442 Combine like terms: -0.3055555556 + 0.4444444442 = 0.1388888886 0.4444444442 + 1.333333333x + x2 = 0.1388888886 Factor a perfect square on the left side: (x + 0.6666666665)(x + 0.6666666665) = 0.1388888886 Calculate the square root of the right side: 0.372677996 Break this problem into two subproblems by setting (x + 0.6666666665) equal to 0.372677996 and -0.372677996.Subproblem 1
x + 0.6666666665 = 0.372677996 Simplifying x + 0.6666666665 = 0.372677996 Reorder the terms: 0.6666666665 + x = 0.372677996 Solving 0.6666666665 + x = 0.372677996 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 = 0.372677996 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = 0.372677996 + -0.6666666665 x = 0.372677996 + -0.6666666665 Combine like terms: 0.372677996 + -0.6666666665 = -0.2939886705 x = -0.2939886705 Simplifying x = -0.2939886705Subproblem 2
x + 0.6666666665 = -0.372677996 Simplifying x + 0.6666666665 = -0.372677996 Reorder the terms: 0.6666666665 + x = -0.372677996 Solving 0.6666666665 + x = -0.372677996 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 = -0.372677996 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = -0.372677996 + -0.6666666665 x = -0.372677996 + -0.6666666665 Combine like terms: -0.372677996 + -0.6666666665 = -1.0393446625 x = -1.0393446625 Simplifying x = -1.0393446625Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.2939886705, -1.0393446625}
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