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Simplifying (3x + 1)(x + 1) = 130 Reorder the terms: (1 + 3x)(x + 1) = 130 Reorder the terms: (1 + 3x)(1 + x) = 130 Multiply (1 + 3x) * (1 + x) (1(1 + x) + 3x * (1 + x)) = 130 ((1 * 1 + x * 1) + 3x * (1 + x)) = 130 ((1 + 1x) + 3x * (1 + x)) = 130 (1 + 1x + (1 * 3x + x * 3x)) = 130 (1 + 1x + (3x + 3x2)) = 130 Combine like terms: 1x + 3x = 4x (1 + 4x + 3x2) = 130 Solving 1 + 4x + 3x2 = 130 Solving for variable 'x'. Reorder the terms: 1 + -130 + 4x + 3x2 = 130 + -130 Combine like terms: 1 + -130 = -129 -129 + 4x + 3x2 = 130 + -130 Combine like terms: 130 + -130 = 0 -129 + 4x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -43 + 1.333333333x + x2 = 0 Move the constant term to the right: Add '43' to each side of the equation. -43 + 1.333333333x + 43 + x2 = 0 + 43 Reorder the terms: -43 + 43 + 1.333333333x + x2 = 0 + 43 Combine like terms: -43 + 43 = 0 0 + 1.333333333x + x2 = 0 + 43 1.333333333x + x2 = 0 + 43 Combine like terms: 0 + 43 = 43 1.333333333x + x2 = 43 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 = 43 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333x + x2 = 43 + 0.4444444442 Combine like terms: 43 + 0.4444444442 = 43.4444444442 0.4444444442 + 1.333333333x + x2 = 43.4444444442 Factor a perfect square on the left side: (x + 0.6666666665)(x + 0.6666666665) = 43.4444444442 Calculate the square root of the right side: 6.591239978 Break this problem into two subproblems by setting (x + 0.6666666665) equal to 6.591239978 and -6.591239978.Subproblem 1
x + 0.6666666665 = 6.591239978 Simplifying x + 0.6666666665 = 6.591239978 Reorder the terms: 0.6666666665 + x = 6.591239978 Solving 0.6666666665 + x = 6.591239978 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 = 6.591239978 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = 6.591239978 + -0.6666666665 x = 6.591239978 + -0.6666666665 Combine like terms: 6.591239978 + -0.6666666665 = 5.9245733115 x = 5.9245733115 Simplifying x = 5.9245733115Subproblem 2
x + 0.6666666665 = -6.591239978 Simplifying x + 0.6666666665 = -6.591239978 Reorder the terms: 0.6666666665 + x = -6.591239978 Solving 0.6666666665 + x = -6.591239978 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 = -6.591239978 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = -6.591239978 + -0.6666666665 x = -6.591239978 + -0.6666666665 Combine like terms: -6.591239978 + -0.6666666665 = -7.2579066445 x = -7.2579066445 Simplifying x = -7.2579066445Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.9245733115, -7.2579066445}
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