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Simplifying 5x(x + 7) = 3x + 17 Reorder the terms: 5x(7 + x) = 3x + 17 (7 * 5x + x * 5x) = 3x + 17 (35x + 5x2) = 3x + 17 Reorder the terms: 35x + 5x2 = 17 + 3x Solving 35x + 5x2 = 17 + 3x Solving for variable 'x'. Reorder the terms: -17 + 35x + -3x + 5x2 = 17 + 3x + -17 + -3x Combine like terms: 35x + -3x = 32x -17 + 32x + 5x2 = 17 + 3x + -17 + -3x Reorder the terms: -17 + 32x + 5x2 = 17 + -17 + 3x + -3x Combine like terms: 17 + -17 = 0 -17 + 32x + 5x2 = 0 + 3x + -3x -17 + 32x + 5x2 = 3x + -3x Combine like terms: 3x + -3x = 0 -17 + 32x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -3.4 + 6.4x + x2 = 0 Move the constant term to the right: Add '3.4' to each side of the equation. -3.4 + 6.4x + 3.4 + x2 = 0 + 3.4 Reorder the terms: -3.4 + 3.4 + 6.4x + x2 = 0 + 3.4 Combine like terms: -3.4 + 3.4 = 0.0 0.0 + 6.4x + x2 = 0 + 3.4 6.4x + x2 = 0 + 3.4 Combine like terms: 0 + 3.4 = 3.4 6.4x + x2 = 3.4 The x term is 6.4x. Take half its coefficient (3.2). Square it (10.24) and add it to both sides. Add '10.24' to each side of the equation. 6.4x + 10.24 + x2 = 3.4 + 10.24 Reorder the terms: 10.24 + 6.4x + x2 = 3.4 + 10.24 Combine like terms: 3.4 + 10.24 = 13.64 10.24 + 6.4x + x2 = 13.64 Factor a perfect square on the left side: (x + 3.2)(x + 3.2) = 13.64 Calculate the square root of the right side: 3.693237063 Break this problem into two subproblems by setting (x + 3.2) equal to 3.693237063 and -3.693237063.Subproblem 1
x + 3.2 = 3.693237063 Simplifying x + 3.2 = 3.693237063 Reorder the terms: 3.2 + x = 3.693237063 Solving 3.2 + x = 3.693237063 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.2' to each side of the equation. 3.2 + -3.2 + x = 3.693237063 + -3.2 Combine like terms: 3.2 + -3.2 = 0.0 0.0 + x = 3.693237063 + -3.2 x = 3.693237063 + -3.2 Combine like terms: 3.693237063 + -3.2 = 0.493237063 x = 0.493237063 Simplifying x = 0.493237063Subproblem 2
x + 3.2 = -3.693237063 Simplifying x + 3.2 = -3.693237063 Reorder the terms: 3.2 + x = -3.693237063 Solving 3.2 + x = -3.693237063 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.2' to each side of the equation. 3.2 + -3.2 + x = -3.693237063 + -3.2 Combine like terms: 3.2 + -3.2 = 0.0 0.0 + x = -3.693237063 + -3.2 x = -3.693237063 + -3.2 Combine like terms: -3.693237063 + -3.2 = -6.893237063 x = -6.893237063 Simplifying x = -6.893237063Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.493237063, -6.893237063}
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