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Simplifying 18 + -10x + 10(3x + 4 + 3x) + -20 + 1x(2x + -12 + 3x) = 0 Reorder the terms: 18 + -10x + 10(4 + 3x + 3x) + -20 + 1x(2x + -12 + 3x) = 0 Combine like terms: 3x + 3x = 6x 18 + -10x + 10(4 + 6x) + -20 + 1x(2x + -12 + 3x) = 0 18 + -10x + (4 * 10 + 6x * 10) + -20 + 1x(2x + -12 + 3x) = 0 18 + -10x + (40 + 60x) + -20 + 1x(2x + -12 + 3x) = 0 Reorder the terms: 18 + -10x + 40 + 60x + -20 + 1x(-12 + 2x + 3x) = 0 Combine like terms: 2x + 3x = 5x 18 + -10x + 40 + 60x + -20 + 1x(-12 + 5x) = 0 18 + -10x + 40 + 60x + -20 + (-12 * 1x + 5x * 1x) = 0 18 + -10x + 40 + 60x + -20 + (-12x + 5x2) = 0 Reorder the terms: 18 + 40 + -20 + -10x + 60x + -12x + 5x2 = 0 Combine like terms: 18 + 40 = 58 58 + -20 + -10x + 60x + -12x + 5x2 = 0 Combine like terms: 58 + -20 = 38 38 + -10x + 60x + -12x + 5x2 = 0 Combine like terms: -10x + 60x = 50x 38 + 50x + -12x + 5x2 = 0 Combine like terms: 50x + -12x = 38x 38 + 38x + 5x2 = 0 Solving 38 + 38x + 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'. 7.6 + 7.6x + x2 = 0 Move the constant term to the right: Add '-7.6' to each side of the equation. 7.6 + 7.6x + -7.6 + x2 = 0 + -7.6 Reorder the terms: 7.6 + -7.6 + 7.6x + x2 = 0 + -7.6 Combine like terms: 7.6 + -7.6 = 0.0 0.0 + 7.6x + x2 = 0 + -7.6 7.6x + x2 = 0 + -7.6 Combine like terms: 0 + -7.6 = -7.6 7.6x + x2 = -7.6 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 = -7.6 + 14.44 Reorder the terms: 14.44 + 7.6x + x2 = -7.6 + 14.44 Combine like terms: -7.6 + 14.44 = 6.84 14.44 + 7.6x + x2 = 6.84 Factor a perfect square on the left side: (x + 3.8)(x + 3.8) = 6.84 Calculate the square root of the right side: 2.615339366 Break this problem into two subproblems by setting (x + 3.8) equal to 2.615339366 and -2.615339366.Subproblem 1
x + 3.8 = 2.615339366 Simplifying x + 3.8 = 2.615339366 Reorder the terms: 3.8 + x = 2.615339366 Solving 3.8 + x = 2.615339366 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 = 2.615339366 + -3.8 Combine like terms: 3.8 + -3.8 = 0.0 0.0 + x = 2.615339366 + -3.8 x = 2.615339366 + -3.8 Combine like terms: 2.615339366 + -3.8 = -1.184660634 x = -1.184660634 Simplifying x = -1.184660634Subproblem 2
x + 3.8 = -2.615339366 Simplifying x + 3.8 = -2.615339366 Reorder the terms: 3.8 + x = -2.615339366 Solving 3.8 + x = -2.615339366 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 = -2.615339366 + -3.8 Combine like terms: 3.8 + -3.8 = 0.0 0.0 + x = -2.615339366 + -3.8 x = -2.615339366 + -3.8 Combine like terms: -2.615339366 + -3.8 = -6.415339366 x = -6.415339366 Simplifying x = -6.415339366Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.184660634, -6.415339366}
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