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Simplifying 18 + -10x + 10(3x + 4 + 3x) + -20 + 1x(2x + -12 + 3) = 0 Reorder the terms: 18 + -10x + 10(4 + 3x + 3x) + -20 + 1x(2x + -12 + 3) = 0 Combine like terms: 3x + 3x = 6x 18 + -10x + 10(4 + 6x) + -20 + 1x(2x + -12 + 3) = 0 18 + -10x + (4 * 10 + 6x * 10) + -20 + 1x(2x + -12 + 3) = 0 18 + -10x + (40 + 60x) + -20 + 1x(2x + -12 + 3) = 0 Reorder the terms: 18 + -10x + 40 + 60x + -20 + 1x(-12 + 3 + 2x) = 0 Combine like terms: -12 + 3 = -9 18 + -10x + 40 + 60x + -20 + 1x(-9 + 2x) = 0 18 + -10x + 40 + 60x + -20 + (-9 * 1x + 2x * 1x) = 0 18 + -10x + 40 + 60x + -20 + (-9x + 2x2) = 0 Reorder the terms: 18 + 40 + -20 + -10x + 60x + -9x + 2x2 = 0 Combine like terms: 18 + 40 = 58 58 + -20 + -10x + 60x + -9x + 2x2 = 0 Combine like terms: 58 + -20 = 38 38 + -10x + 60x + -9x + 2x2 = 0 Combine like terms: -10x + 60x = 50x 38 + 50x + -9x + 2x2 = 0 Combine like terms: 50x + -9x = 41x 38 + 41x + 2x2 = 0 Solving 38 + 41x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 19 + 20.5x + x2 = 0 Move the constant term to the right: Add '-19' to each side of the equation. 19 + 20.5x + -19 + x2 = 0 + -19 Reorder the terms: 19 + -19 + 20.5x + x2 = 0 + -19 Combine like terms: 19 + -19 = 0 0 + 20.5x + x2 = 0 + -19 20.5x + x2 = 0 + -19 Combine like terms: 0 + -19 = -19 20.5x + x2 = -19 The x term is 20.5x. Take half its coefficient (10.25). Square it (105.0625) and add it to both sides. Add '105.0625' to each side of the equation. 20.5x + 105.0625 + x2 = -19 + 105.0625 Reorder the terms: 105.0625 + 20.5x + x2 = -19 + 105.0625 Combine like terms: -19 + 105.0625 = 86.0625 105.0625 + 20.5x + x2 = 86.0625 Factor a perfect square on the left side: (x + 10.25)(x + 10.25) = 86.0625 Calculate the square root of the right side: 9.276987658 Break this problem into two subproblems by setting (x + 10.25) equal to 9.276987658 and -9.276987658.Subproblem 1
x + 10.25 = 9.276987658 Simplifying x + 10.25 = 9.276987658 Reorder the terms: 10.25 + x = 9.276987658 Solving 10.25 + x = 9.276987658 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.25' to each side of the equation. 10.25 + -10.25 + x = 9.276987658 + -10.25 Combine like terms: 10.25 + -10.25 = 0.00 0.00 + x = 9.276987658 + -10.25 x = 9.276987658 + -10.25 Combine like terms: 9.276987658 + -10.25 = -0.973012342 x = -0.973012342 Simplifying x = -0.973012342Subproblem 2
x + 10.25 = -9.276987658 Simplifying x + 10.25 = -9.276987658 Reorder the terms: 10.25 + x = -9.276987658 Solving 10.25 + x = -9.276987658 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.25' to each side of the equation. 10.25 + -10.25 + x = -9.276987658 + -10.25 Combine like terms: 10.25 + -10.25 = 0.00 0.00 + x = -9.276987658 + -10.25 x = -9.276987658 + -10.25 Combine like terms: -9.276987658 + -10.25 = -19.526987658 x = -19.526987658 Simplifying x = -19.526987658Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.973012342, -19.526987658}
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