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Simplifying 2x(3 + -1x) + -4(x + 2) = 3x(2x + -3x) + 5 + 7x * -12 (3 * 2x + -1x * 2x) + -4(x + 2) = 3x(2x + -3x) + 5 + 7x * -12 (6x + -2x2) + -4(x + 2) = 3x(2x + -3x) + 5 + 7x * -12 Reorder the terms: 6x + -2x2 + -4(2 + x) = 3x(2x + -3x) + 5 + 7x * -12 6x + -2x2 + (2 * -4 + x * -4) = 3x(2x + -3x) + 5 + 7x * -12 6x + -2x2 + (-8 + -4x) = 3x(2x + -3x) + 5 + 7x * -12 Reorder the terms: -8 + 6x + -4x + -2x2 = 3x(2x + -3x) + 5 + 7x * -12 Combine like terms: 6x + -4x = 2x -8 + 2x + -2x2 = 3x(2x + -3x) + 5 + 7x * -12 Combine like terms: 2x + -3x = -1x -8 + 2x + -2x2 = 3x(-1x) + 5 + 7x * -12 Remove parenthesis around (-1x) -8 + 2x + -2x2 = 3x * -1x + 5 + 7x * -12 Reorder the terms for easier multiplication: -8 + 2x + -2x2 = 3 * -1x * x + 5 + 7x * -12 Multiply 3 * -1 -8 + 2x + -2x2 = -3x * x + 5 + 7x * -12 Multiply x * x -8 + 2x + -2x2 = -3x2 + 5 + 7x * -12 Reorder the terms for easier multiplication: -8 + 2x + -2x2 = -3x2 + 5 + 7 * -12x Multiply 7 * -12 -8 + 2x + -2x2 = -3x2 + 5 + -84x Reorder the terms: -8 + 2x + -2x2 = 5 + -84x + -3x2 Solving -8 + 2x + -2x2 = 5 + -84x + -3x2 Solving for variable 'x'. Reorder the terms: -8 + -5 + 2x + 84x + -2x2 + 3x2 = 5 + -84x + -3x2 + -5 + 84x + 3x2 Combine like terms: -8 + -5 = -13 -13 + 2x + 84x + -2x2 + 3x2 = 5 + -84x + -3x2 + -5 + 84x + 3x2 Combine like terms: 2x + 84x = 86x -13 + 86x + -2x2 + 3x2 = 5 + -84x + -3x2 + -5 + 84x + 3x2 Combine like terms: -2x2 + 3x2 = 1x2 -13 + 86x + 1x2 = 5 + -84x + -3x2 + -5 + 84x + 3x2 Reorder the terms: -13 + 86x + 1x2 = 5 + -5 + -84x + 84x + -3x2 + 3x2 Combine like terms: 5 + -5 = 0 -13 + 86x + 1x2 = 0 + -84x + 84x + -3x2 + 3x2 -13 + 86x + 1x2 = -84x + 84x + -3x2 + 3x2 Combine like terms: -84x + 84x = 0 -13 + 86x + 1x2 = 0 + -3x2 + 3x2 -13 + 86x + 1x2 = -3x2 + 3x2 Combine like terms: -3x2 + 3x2 = 0 -13 + 86x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '13' to each side of the equation. -13 + 86x + 13 + x2 = 0 + 13 Reorder the terms: -13 + 13 + 86x + x2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + 86x + x2 = 0 + 13 86x + x2 = 0 + 13 Combine like terms: 0 + 13 = 13 86x + x2 = 13 The x term is 86x. Take half its coefficient (43). Square it (1849) and add it to both sides. Add '1849' to each side of the equation. 86x + 1849 + x2 = 13 + 1849 Reorder the terms: 1849 + 86x + x2 = 13 + 1849 Combine like terms: 13 + 1849 = 1862 1849 + 86x + x2 = 1862 Factor a perfect square on the left side: (x + 43)(x + 43) = 1862 Calculate the square root of the right side: 43.150898021 Break this problem into two subproblems by setting (x + 43) equal to 43.150898021 and -43.150898021.Subproblem 1
x + 43 = 43.150898021 Simplifying x + 43 = 43.150898021 Reorder the terms: 43 + x = 43.150898021 Solving 43 + x = 43.150898021 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-43' to each side of the equation. 43 + -43 + x = 43.150898021 + -43 Combine like terms: 43 + -43 = 0 0 + x = 43.150898021 + -43 x = 43.150898021 + -43 Combine like terms: 43.150898021 + -43 = 0.150898021 x = 0.150898021 Simplifying x = 0.150898021Subproblem 2
x + 43 = -43.150898021 Simplifying x + 43 = -43.150898021 Reorder the terms: 43 + x = -43.150898021 Solving 43 + x = -43.150898021 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-43' to each side of the equation. 43 + -43 + x = -43.150898021 + -43 Combine like terms: 43 + -43 = 0 0 + x = -43.150898021 + -43 x = -43.150898021 + -43 Combine like terms: -43.150898021 + -43 = -86.150898021 x = -86.150898021 Simplifying x = -86.150898021Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.150898021, -86.150898021}
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