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Simplifying 3x(x + 1) + (x + 2) = 8 Reorder the terms: 3x(1 + x) + (x + 2) = 8 (1 * 3x + x * 3x) + (x + 2) = 8 (3x + 3x2) + (x + 2) = 8 Reorder the terms: 3x + 3x2 + (2 + x) = 8 Remove parenthesis around (2 + x) 3x + 3x2 + 2 + x = 8 Reorder the terms: 2 + 3x + x + 3x2 = 8 Combine like terms: 3x + x = 4x 2 + 4x + 3x2 = 8 Solving 2 + 4x + 3x2 = 8 Solving for variable 'x'. Reorder the terms: 2 + -8 + 4x + 3x2 = 8 + -8 Combine like terms: 2 + -8 = -6 -6 + 4x + 3x2 = 8 + -8 Combine like terms: 8 + -8 = 0 -6 + 4x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -2 + 1.333333333x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 1.333333333x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + 1.333333333x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 1.333333333x + x2 = 0 + 2 1.333333333x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 1.333333333x + x2 = 2 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 = 2 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333x + x2 = 2 + 0.4444444442 Combine like terms: 2 + 0.4444444442 = 2.4444444442 0.4444444442 + 1.333333333x + x2 = 2.4444444442 Factor a perfect square on the left side: (x + 0.6666666665)(x + 0.6666666665) = 2.4444444442 Calculate the square root of the right side: 1.56347192 Break this problem into two subproblems by setting (x + 0.6666666665) equal to 1.56347192 and -1.56347192.Subproblem 1
x + 0.6666666665 = 1.56347192 Simplifying x + 0.6666666665 = 1.56347192 Reorder the terms: 0.6666666665 + x = 1.56347192 Solving 0.6666666665 + x = 1.56347192 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 = 1.56347192 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = 1.56347192 + -0.6666666665 x = 1.56347192 + -0.6666666665 Combine like terms: 1.56347192 + -0.6666666665 = 0.8968052535 x = 0.8968052535 Simplifying x = 0.8968052535Subproblem 2
x + 0.6666666665 = -1.56347192 Simplifying x + 0.6666666665 = -1.56347192 Reorder the terms: 0.6666666665 + x = -1.56347192 Solving 0.6666666665 + x = -1.56347192 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 = -1.56347192 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = -1.56347192 + -0.6666666665 x = -1.56347192 + -0.6666666665 Combine like terms: -1.56347192 + -0.6666666665 = -2.2301385865 x = -2.2301385865 Simplifying x = -2.2301385865Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8968052535, -2.2301385865}
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