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Simplifying (2x + 3)(x) = 400 Reorder the terms: (3 + 2x)(x) = 400 Reorder the terms for easier multiplication: x(3 + 2x) = 400 (3 * x + 2x * x) = 400 (3x + 2x2) = 400 Solving 3x + 2x2 = 400 Solving for variable 'x'. Reorder the terms: -400 + 3x + 2x2 = 400 + -400 Combine like terms: 400 + -400 = 0 -400 + 3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -200 + 1.5x + x2 = 0 Move the constant term to the right: Add '200' to each side of the equation. -200 + 1.5x + 200 + x2 = 0 + 200 Reorder the terms: -200 + 200 + 1.5x + x2 = 0 + 200 Combine like terms: -200 + 200 = 0 0 + 1.5x + x2 = 0 + 200 1.5x + x2 = 0 + 200 Combine like terms: 0 + 200 = 200 1.5x + x2 = 200 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 = 200 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 200 + 0.5625 Combine like terms: 200 + 0.5625 = 200.5625 0.5625 + 1.5x + x2 = 200.5625 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 200.5625 Calculate the square root of the right side: 14.162009038 Break this problem into two subproblems by setting (x + 0.75) equal to 14.162009038 and -14.162009038.Subproblem 1
x + 0.75 = 14.162009038 Simplifying x + 0.75 = 14.162009038 Reorder the terms: 0.75 + x = 14.162009038 Solving 0.75 + x = 14.162009038 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 = 14.162009038 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 14.162009038 + -0.75 x = 14.162009038 + -0.75 Combine like terms: 14.162009038 + -0.75 = 13.412009038 x = 13.412009038 Simplifying x = 13.412009038Subproblem 2
x + 0.75 = -14.162009038 Simplifying x + 0.75 = -14.162009038 Reorder the terms: 0.75 + x = -14.162009038 Solving 0.75 + x = -14.162009038 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 = -14.162009038 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -14.162009038 + -0.75 x = -14.162009038 + -0.75 Combine like terms: -14.162009038 + -0.75 = -14.912009038 x = -14.912009038 Simplifying x = -14.912009038Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.412009038, -14.912009038}
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