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Simplifying (2x + 1) * 3x + 2 = 24 Reorder the terms: (1 + 2x) * 3x + 2 = 24 Reorder the terms for easier multiplication: 3x(1 + 2x) + 2 = 24 (1 * 3x + 2x * 3x) + 2 = 24 (3x + 6x2) + 2 = 24 Reorder the terms: 2 + 3x + 6x2 = 24 Solving 2 + 3x + 6x2 = 24 Solving for variable 'x'. Reorder the terms: 2 + -24 + 3x + 6x2 = 24 + -24 Combine like terms: 2 + -24 = -22 -22 + 3x + 6x2 = 24 + -24 Combine like terms: 24 + -24 = 0 -22 + 3x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -3.666666667 + 0.5x + x2 = 0 Move the constant term to the right: Add '3.666666667' to each side of the equation. -3.666666667 + 0.5x + 3.666666667 + x2 = 0 + 3.666666667 Reorder the terms: -3.666666667 + 3.666666667 + 0.5x + x2 = 0 + 3.666666667 Combine like terms: -3.666666667 + 3.666666667 = 0.000000000 0.000000000 + 0.5x + x2 = 0 + 3.666666667 0.5x + x2 = 0 + 3.666666667 Combine like terms: 0 + 3.666666667 = 3.666666667 0.5x + x2 = 3.666666667 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = 3.666666667 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 3.666666667 + 0.0625 Combine like terms: 3.666666667 + 0.0625 = 3.729166667 0.0625 + 0.5x + x2 = 3.729166667 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 3.729166667 Calculate the square root of the right side: 1.931105038 Break this problem into two subproblems by setting (x + 0.25) equal to 1.931105038 and -1.931105038.Subproblem 1
x + 0.25 = 1.931105038 Simplifying x + 0.25 = 1.931105038 Reorder the terms: 0.25 + x = 1.931105038 Solving 0.25 + x = 1.931105038 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 1.931105038 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 1.931105038 + -0.25 x = 1.931105038 + -0.25 Combine like terms: 1.931105038 + -0.25 = 1.681105038 x = 1.681105038 Simplifying x = 1.681105038Subproblem 2
x + 0.25 = -1.931105038 Simplifying x + 0.25 = -1.931105038 Reorder the terms: 0.25 + x = -1.931105038 Solving 0.25 + x = -1.931105038 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -1.931105038 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -1.931105038 + -0.25 x = -1.931105038 + -0.25 Combine like terms: -1.931105038 + -0.25 = -2.181105038 x = -2.181105038 Simplifying x = -2.181105038Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.681105038, -2.181105038}
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