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Simplifying 6(2x + -5) = -1x(x + -4) Reorder the terms: 6(-5 + 2x) = -1x(x + -4) (-5 * 6 + 2x * 6) = -1x(x + -4) (-30 + 12x) = -1x(x + -4) Reorder the terms: -30 + 12x = -1x(-4 + x) -30 + 12x = (-4 * -1x + x * -1x) -30 + 12x = (4x + -1x2) Solving -30 + 12x = 4x + -1x2 Solving for variable 'x'. Combine like terms: 12x + -4x = 8x -30 + 8x + x2 = 4x + -1x2 + -4x + x2 Reorder the terms: -30 + 8x + x2 = 4x + -4x + -1x2 + x2 Combine like terms: 4x + -4x = 0 -30 + 8x + x2 = 0 + -1x2 + x2 -30 + 8x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -30 + 8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '30' to each side of the equation. -30 + 8x + 30 + x2 = 0 + 30 Reorder the terms: -30 + 30 + 8x + x2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + 8x + x2 = 0 + 30 8x + x2 = 0 + 30 Combine like terms: 0 + 30 = 30 8x + x2 = 30 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = 30 + 16 Reorder the terms: 16 + 8x + x2 = 30 + 16 Combine like terms: 30 + 16 = 46 16 + 8x + x2 = 46 Factor a perfect square on the left side: (x + 4)(x + 4) = 46 Calculate the square root of the right side: 6.782329983 Break this problem into two subproblems by setting (x + 4) equal to 6.782329983 and -6.782329983.Subproblem 1
x + 4 = 6.782329983 Simplifying x + 4 = 6.782329983 Reorder the terms: 4 + x = 6.782329983 Solving 4 + x = 6.782329983 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 6.782329983 + -4 Combine like terms: 4 + -4 = 0 0 + x = 6.782329983 + -4 x = 6.782329983 + -4 Combine like terms: 6.782329983 + -4 = 2.782329983 x = 2.782329983 Simplifying x = 2.782329983Subproblem 2
x + 4 = -6.782329983 Simplifying x + 4 = -6.782329983 Reorder the terms: 4 + x = -6.782329983 Solving 4 + x = -6.782329983 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -6.782329983 + -4 Combine like terms: 4 + -4 = 0 0 + x = -6.782329983 + -4 x = -6.782329983 + -4 Combine like terms: -6.782329983 + -4 = -10.782329983 x = -10.782329983 Simplifying x = -10.782329983Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.782329983, -10.782329983}
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