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Simplifying (2x + 3)(x) = 184 Reorder the terms: (3 + 2x)(x) = 184 Reorder the terms for easier multiplication: x(3 + 2x) = 184 (3 * x + 2x * x) = 184 (3x + 2x2) = 184 Solving 3x + 2x2 = 184 Solving for variable 'x'. Reorder the terms: -184 + 3x + 2x2 = 184 + -184 Combine like terms: 184 + -184 = 0 -184 + 3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -92 + 1.5x + x2 = 0 Move the constant term to the right: Add '92' to each side of the equation. -92 + 1.5x + 92 + x2 = 0 + 92 Reorder the terms: -92 + 92 + 1.5x + x2 = 0 + 92 Combine like terms: -92 + 92 = 0 0 + 1.5x + x2 = 0 + 92 1.5x + x2 = 0 + 92 Combine like terms: 0 + 92 = 92 1.5x + x2 = 92 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = 92 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 92 + 0.5625 Combine like terms: 92 + 0.5625 = 92.5625 0.5625 + 1.5x + x2 = 92.5625 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 92.5625 Calculate the square root of the right side: 9.620940702 Break this problem into two subproblems by setting (x + 0.75) equal to 9.620940702 and -9.620940702.Subproblem 1
x + 0.75 = 9.620940702 Simplifying x + 0.75 = 9.620940702 Reorder the terms: 0.75 + x = 9.620940702 Solving 0.75 + x = 9.620940702 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 9.620940702 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 9.620940702 + -0.75 x = 9.620940702 + -0.75 Combine like terms: 9.620940702 + -0.75 = 8.870940702 x = 8.870940702 Simplifying x = 8.870940702Subproblem 2
x + 0.75 = -9.620940702 Simplifying x + 0.75 = -9.620940702 Reorder the terms: 0.75 + x = -9.620940702 Solving 0.75 + x = -9.620940702 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -9.620940702 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -9.620940702 + -0.75 x = -9.620940702 + -0.75 Combine like terms: -9.620940702 + -0.75 = -10.370940702 x = -10.370940702 Simplifying x = -10.370940702Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.870940702, -10.370940702}
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