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Simplifying (2x + 3) * x + 5 + 3x(x + 5) + x = 0 Reorder the terms: (3 + 2x) * x + 5 + 3x(x + 5) + x = 0 Reorder the terms for easier multiplication: x(3 + 2x) + 5 + 3x(x + 5) + x = 0 (3 * x + 2x * x) + 5 + 3x(x + 5) + x = 0 (3x + 2x2) + 5 + 3x(x + 5) + x = 0 Reorder the terms: 3x + 2x2 + 5 + 3x(5 + x) + x = 0 3x + 2x2 + 5 + (5 * 3x + x * 3x) + x = 0 3x + 2x2 + 5 + (15x + 3x2) + x = 0 Reorder the terms: 5 + 3x + 15x + x + 2x2 + 3x2 = 0 Combine like terms: 3x + 15x = 18x 5 + 18x + x + 2x2 + 3x2 = 0 Combine like terms: 18x + x = 19x 5 + 19x + 2x2 + 3x2 = 0 Combine like terms: 2x2 + 3x2 = 5x2 5 + 19x + 5x2 = 0 Solving 5 + 19x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1 + 3.8x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + 3.8x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + 3.8x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3.8x + x2 = 0 + -1 3.8x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 3.8x + x2 = -1 The x term is 3.8x. Take half its coefficient (1.9). Square it (3.61) and add it to both sides. Add '3.61' to each side of the equation. 3.8x + 3.61 + x2 = -1 + 3.61 Reorder the terms: 3.61 + 3.8x + x2 = -1 + 3.61 Combine like terms: -1 + 3.61 = 2.61 3.61 + 3.8x + x2 = 2.61 Factor a perfect square on the left side: (x + 1.9)(x + 1.9) = 2.61 Calculate the square root of the right side: 1.615549442 Break this problem into two subproblems by setting (x + 1.9) equal to 1.615549442 and -1.615549442.Subproblem 1
x + 1.9 = 1.615549442 Simplifying x + 1.9 = 1.615549442 Reorder the terms: 1.9 + x = 1.615549442 Solving 1.9 + x = 1.615549442 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.9' to each side of the equation. 1.9 + -1.9 + x = 1.615549442 + -1.9 Combine like terms: 1.9 + -1.9 = 0.0 0.0 + x = 1.615549442 + -1.9 x = 1.615549442 + -1.9 Combine like terms: 1.615549442 + -1.9 = -0.284450558 x = -0.284450558 Simplifying x = -0.284450558Subproblem 2
x + 1.9 = -1.615549442 Simplifying x + 1.9 = -1.615549442 Reorder the terms: 1.9 + x = -1.615549442 Solving 1.9 + x = -1.615549442 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.9' to each side of the equation. 1.9 + -1.9 + x = -1.615549442 + -1.9 Combine like terms: 1.9 + -1.9 = 0.0 0.0 + x = -1.615549442 + -1.9 x = -1.615549442 + -1.9 Combine like terms: -1.615549442 + -1.9 = -3.515549442 x = -3.515549442 Simplifying x = -3.515549442Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.284450558, -3.515549442}
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