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Simplifying 3x + -10 + 2x + 5 + 2x(2x + 5) = 185 Reorder the terms: 3x + -10 + 2x + 5 + 2x(5 + 2x) = 185 3x + -10 + 2x + 5 + (5 * 2x + 2x * 2x) = 185 3x + -10 + 2x + 5 + (10x + 4x2) = 185 Reorder the terms: -10 + 5 + 3x + 2x + 10x + 4x2 = 185 Combine like terms: -10 + 5 = -5 -5 + 3x + 2x + 10x + 4x2 = 185 Combine like terms: 3x + 2x = 5x -5 + 5x + 10x + 4x2 = 185 Combine like terms: 5x + 10x = 15x -5 + 15x + 4x2 = 185 Solving -5 + 15x + 4x2 = 185 Solving for variable 'x'. Reorder the terms: -5 + -185 + 15x + 4x2 = 185 + -185 Combine like terms: -5 + -185 = -190 -190 + 15x + 4x2 = 185 + -185 Combine like terms: 185 + -185 = 0 -190 + 15x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -47.5 + 3.75x + x2 = 0 Move the constant term to the right: Add '47.5' to each side of the equation. -47.5 + 3.75x + 47.5 + x2 = 0 + 47.5 Reorder the terms: -47.5 + 47.5 + 3.75x + x2 = 0 + 47.5 Combine like terms: -47.5 + 47.5 = 0.0 0.0 + 3.75x + x2 = 0 + 47.5 3.75x + x2 = 0 + 47.5 Combine like terms: 0 + 47.5 = 47.5 3.75x + x2 = 47.5 The x term is 3.75x. Take half its coefficient (1.875). Square it (3.515625) and add it to both sides. Add '3.515625' to each side of the equation. 3.75x + 3.515625 + x2 = 47.5 + 3.515625 Reorder the terms: 3.515625 + 3.75x + x2 = 47.5 + 3.515625 Combine like terms: 47.5 + 3.515625 = 51.015625 3.515625 + 3.75x + x2 = 51.015625 Factor a perfect square on the left side: (x + 1.875)(x + 1.875) = 51.015625 Calculate the square root of the right side: 7.142522314 Break this problem into two subproblems by setting (x + 1.875) equal to 7.142522314 and -7.142522314.Subproblem 1
x + 1.875 = 7.142522314 Simplifying x + 1.875 = 7.142522314 Reorder the terms: 1.875 + x = 7.142522314 Solving 1.875 + x = 7.142522314 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.875' to each side of the equation. 1.875 + -1.875 + x = 7.142522314 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + x = 7.142522314 + -1.875 x = 7.142522314 + -1.875 Combine like terms: 7.142522314 + -1.875 = 5.267522314 x = 5.267522314 Simplifying x = 5.267522314Subproblem 2
x + 1.875 = -7.142522314 Simplifying x + 1.875 = -7.142522314 Reorder the terms: 1.875 + x = -7.142522314 Solving 1.875 + x = -7.142522314 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.875' to each side of the equation. 1.875 + -1.875 + x = -7.142522314 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + x = -7.142522314 + -1.875 x = -7.142522314 + -1.875 Combine like terms: -7.142522314 + -1.875 = -9.017522314 x = -9.017522314 Simplifying x = -9.017522314Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.267522314, -9.017522314}
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