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Simplifying x(2x + 3) = 6 Reorder the terms: x(3 + 2x) = 6 (3 * x + 2x * x) = 6 (3x + 2x2) = 6 Solving 3x + 2x2 = 6 Solving for variable 'x'. Reorder the terms: -6 + 3x + 2x2 = 6 + -6 Combine like terms: 6 + -6 = 0 -6 + 3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -3 + 1.5x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 1.5x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + 1.5x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 1.5x + x2 = 0 + 3 1.5x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 1.5x + x2 = 3 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 = 3 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 3 + 0.5625 Combine like terms: 3 + 0.5625 = 3.5625 0.5625 + 1.5x + x2 = 3.5625 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 3.5625 Calculate the square root of the right side: 1.887458609 Break this problem into two subproblems by setting (x + 0.75) equal to 1.887458609 and -1.887458609.Subproblem 1
x + 0.75 = 1.887458609 Simplifying x + 0.75 = 1.887458609 Reorder the terms: 0.75 + x = 1.887458609 Solving 0.75 + x = 1.887458609 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 = 1.887458609 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 1.887458609 + -0.75 x = 1.887458609 + -0.75 Combine like terms: 1.887458609 + -0.75 = 1.137458609 x = 1.137458609 Simplifying x = 1.137458609Subproblem 2
x + 0.75 = -1.887458609 Simplifying x + 0.75 = -1.887458609 Reorder the terms: 0.75 + x = -1.887458609 Solving 0.75 + x = -1.887458609 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 = -1.887458609 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -1.887458609 + -0.75 x = -1.887458609 + -0.75 Combine like terms: -1.887458609 + -0.75 = -2.637458609 x = -2.637458609 Simplifying x = -2.637458609Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.137458609, -2.637458609}
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