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Simplifying (5x + 2)(x) = 32 * 3 Reorder the terms: (2 + 5x)(x) = 32 * 3 Reorder the terms for easier multiplication: x(2 + 5x) = 32 * 3 (2 * x + 5x * x) = 32 * 3 (2x + 5x2) = 32 * 3 Multiply 32 * 3 2x + 5x2 = 96 Solving 2x + 5x2 = 96 Solving for variable 'x'. Reorder the terms: -96 + 2x + 5x2 = 96 + -96 Combine like terms: 96 + -96 = 0 -96 + 2x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -19.2 + 0.4x + x2 = 0 Move the constant term to the right: Add '19.2' to each side of the equation. -19.2 + 0.4x + 19.2 + x2 = 0 + 19.2 Reorder the terms: -19.2 + 19.2 + 0.4x + x2 = 0 + 19.2 Combine like terms: -19.2 + 19.2 = 0.0 0.0 + 0.4x + x2 = 0 + 19.2 0.4x + x2 = 0 + 19.2 Combine like terms: 0 + 19.2 = 19.2 0.4x + x2 = 19.2 The x term is 0.4x. Take half its coefficient (0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. 0.4x + 0.04 + x2 = 19.2 + 0.04 Reorder the terms: 0.04 + 0.4x + x2 = 19.2 + 0.04 Combine like terms: 19.2 + 0.04 = 19.24 0.04 + 0.4x + x2 = 19.24 Factor a perfect square on the left side: (x + 0.2)(x + 0.2) = 19.24 Calculate the square root of the right side: 4.38634244 Break this problem into two subproblems by setting (x + 0.2) equal to 4.38634244 and -4.38634244.Subproblem 1
x + 0.2 = 4.38634244 Simplifying x + 0.2 = 4.38634244 Reorder the terms: 0.2 + x = 4.38634244 Solving 0.2 + x = 4.38634244 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = 4.38634244 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = 4.38634244 + -0.2 x = 4.38634244 + -0.2 Combine like terms: 4.38634244 + -0.2 = 4.18634244 x = 4.18634244 Simplifying x = 4.18634244Subproblem 2
x + 0.2 = -4.38634244 Simplifying x + 0.2 = -4.38634244 Reorder the terms: 0.2 + x = -4.38634244 Solving 0.2 + x = -4.38634244 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = -4.38634244 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = -4.38634244 + -0.2 x = -4.38634244 + -0.2 Combine like terms: -4.38634244 + -0.2 = -4.58634244 x = -4.58634244 Simplifying x = -4.58634244Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.18634244, -4.58634244}
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