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Simplifying 35x2 + 302x + -124 = 3 + -5x2 + -2x Reorder the terms: -124 + 302x + 35x2 = 3 + -5x2 + -2x Reorder the terms: -124 + 302x + 35x2 = 3 + -2x + -5x2 Solving -124 + 302x + 35x2 = 3 + -2x + -5x2 Solving for variable 'x'. Reorder the terms: -124 + -3 + 302x + 2x + 35x2 + 5x2 = 3 + -2x + -5x2 + -3 + 2x + 5x2 Combine like terms: -124 + -3 = -127 -127 + 302x + 2x + 35x2 + 5x2 = 3 + -2x + -5x2 + -3 + 2x + 5x2 Combine like terms: 302x + 2x = 304x -127 + 304x + 35x2 + 5x2 = 3 + -2x + -5x2 + -3 + 2x + 5x2 Combine like terms: 35x2 + 5x2 = 40x2 -127 + 304x + 40x2 = 3 + -2x + -5x2 + -3 + 2x + 5x2 Reorder the terms: -127 + 304x + 40x2 = 3 + -3 + -2x + 2x + -5x2 + 5x2 Combine like terms: 3 + -3 = 0 -127 + 304x + 40x2 = 0 + -2x + 2x + -5x2 + 5x2 -127 + 304x + 40x2 = -2x + 2x + -5x2 + 5x2 Combine like terms: -2x + 2x = 0 -127 + 304x + 40x2 = 0 + -5x2 + 5x2 -127 + 304x + 40x2 = -5x2 + 5x2 Combine like terms: -5x2 + 5x2 = 0 -127 + 304x + 40x2 = 0 Begin completing the square. Divide all terms by 40 the coefficient of the squared term: Divide each side by '40'. -3.175 + 7.6x + x2 = 0.0 Move the constant term to the right: Add '3.175' to each side of the equation. -3.175 + 7.6x + 3.175 + x2 = 0.0 + 3.175 Reorder the terms: -3.175 + 3.175 + 7.6x + x2 = 0.0 + 3.175 Combine like terms: -3.175 + 3.175 = 0.000 0.000 + 7.6x + x2 = 0.0 + 3.175 7.6x + x2 = 0.0 + 3.175 Combine like terms: 0.0 + 3.175 = 3.175 7.6x + x2 = 3.175 The x term is 7.6x. Take half its coefficient (3.8). Square it (14.44) and add it to both sides. Add '14.44' to each side of the equation. 7.6x + 14.44 + x2 = 3.175 + 14.44 Reorder the terms: 14.44 + 7.6x + x2 = 3.175 + 14.44 Combine like terms: 3.175 + 14.44 = 17.615 14.44 + 7.6x + x2 = 17.615 Factor a perfect square on the left side: (x + 3.8)(x + 3.8) = 17.615 Calculate the square root of the right side: 4.197022754 Break this problem into two subproblems by setting (x + 3.8) equal to 4.197022754 and -4.197022754.Subproblem 1
x + 3.8 = 4.197022754 Simplifying x + 3.8 = 4.197022754 Reorder the terms: 3.8 + x = 4.197022754 Solving 3.8 + x = 4.197022754 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.8' to each side of the equation. 3.8 + -3.8 + x = 4.197022754 + -3.8 Combine like terms: 3.8 + -3.8 = 0.0 0.0 + x = 4.197022754 + -3.8 x = 4.197022754 + -3.8 Combine like terms: 4.197022754 + -3.8 = 0.397022754 x = 0.397022754 Simplifying x = 0.397022754Subproblem 2
x + 3.8 = -4.197022754 Simplifying x + 3.8 = -4.197022754 Reorder the terms: 3.8 + x = -4.197022754 Solving 3.8 + x = -4.197022754 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.8' to each side of the equation. 3.8 + -3.8 + x = -4.197022754 + -3.8 Combine like terms: 3.8 + -3.8 = 0.0 0.0 + x = -4.197022754 + -3.8 x = -4.197022754 + -3.8 Combine like terms: -4.197022754 + -3.8 = -7.997022754 x = -7.997022754 Simplifying x = -7.997022754Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.397022754, -7.997022754}
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