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Simplifying 5x(x + -4) + 3x + -9x = 6 + -1(2x + 5) + 8x Reorder the terms: 5x(-4 + x) + 3x + -9x = 6 + -1(2x + 5) + 8x (-4 * 5x + x * 5x) + 3x + -9x = 6 + -1(2x + 5) + 8x (-20x + 5x2) + 3x + -9x = 6 + -1(2x + 5) + 8x Reorder the terms: -20x + 3x + -9x + 5x2 = 6 + -1(2x + 5) + 8x Combine like terms: -20x + 3x = -17x -17x + -9x + 5x2 = 6 + -1(2x + 5) + 8x Combine like terms: -17x + -9x = -26x -26x + 5x2 = 6 + -1(2x + 5) + 8x Reorder the terms: -26x + 5x2 = 6 + -1(5 + 2x) + 8x -26x + 5x2 = 6 + (5 * -1 + 2x * -1) + 8x -26x + 5x2 = 6 + (-5 + -2x) + 8x Combine like terms: 6 + -5 = 1 -26x + 5x2 = 1 + -2x + 8x Combine like terms: -2x + 8x = 6x -26x + 5x2 = 1 + 6x Solving -26x + 5x2 = 1 + 6x Solving for variable 'x'. Reorder the terms: -1 + -26x + -6x + 5x2 = 1 + 6x + -1 + -6x Combine like terms: -26x + -6x = -32x -1 + -32x + 5x2 = 1 + 6x + -1 + -6x Reorder the terms: -1 + -32x + 5x2 = 1 + -1 + 6x + -6x Combine like terms: 1 + -1 = 0 -1 + -32x + 5x2 = 0 + 6x + -6x -1 + -32x + 5x2 = 6x + -6x Combine like terms: 6x + -6x = 0 -1 + -32x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.2 + -6.4x + x2 = 0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + -6.4x + 0.2 + x2 = 0 + 0.2 Reorder the terms: -0.2 + 0.2 + -6.4x + x2 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + -6.4x + x2 = 0 + 0.2 -6.4x + x2 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 -6.4x + x2 = 0.2 The x term is -6.4x. Take half its coefficient (-3.2). Square it (10.24) and add it to both sides. Add '10.24' to each side of the equation. -6.4x + 10.24 + x2 = 0.2 + 10.24 Reorder the terms: 10.24 + -6.4x + x2 = 0.2 + 10.24 Combine like terms: 0.2 + 10.24 = 10.44 10.24 + -6.4x + x2 = 10.44 Factor a perfect square on the left side: (x + -3.2)(x + -3.2) = 10.44 Calculate the square root of the right side: 3.231098884 Break this problem into two subproblems by setting (x + -3.2) equal to 3.231098884 and -3.231098884.Subproblem 1
x + -3.2 = 3.231098884 Simplifying x + -3.2 = 3.231098884 Reorder the terms: -3.2 + x = 3.231098884 Solving -3.2 + x = 3.231098884 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.2' to each side of the equation. -3.2 + 3.2 + x = 3.231098884 + 3.2 Combine like terms: -3.2 + 3.2 = 0.0 0.0 + x = 3.231098884 + 3.2 x = 3.231098884 + 3.2 Combine like terms: 3.231098884 + 3.2 = 6.431098884 x = 6.431098884 Simplifying x = 6.431098884Subproblem 2
x + -3.2 = -3.231098884 Simplifying x + -3.2 = -3.231098884 Reorder the terms: -3.2 + x = -3.231098884 Solving -3.2 + x = -3.231098884 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.2' to each side of the equation. -3.2 + 3.2 + x = -3.231098884 + 3.2 Combine like terms: -3.2 + 3.2 = 0.0 0.0 + x = -3.231098884 + 3.2 x = -3.231098884 + 3.2 Combine like terms: -3.231098884 + 3.2 = -0.031098884 x = -0.031098884 Simplifying x = -0.031098884Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.431098884, -0.031098884}
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