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Simplifying (x) = (2x + -1)(x + -5) x = (2x + -1)(x + -5) Reorder the terms: x = (-1 + 2x)(x + -5) Reorder the terms: x = (-1 + 2x)(-5 + x) Multiply (-1 + 2x) * (-5 + x) x = (-1(-5 + x) + 2x * (-5 + x)) x = ((-5 * -1 + x * -1) + 2x * (-5 + x)) x = ((5 + -1x) + 2x * (-5 + x)) x = (5 + -1x + (-5 * 2x + x * 2x)) x = (5 + -1x + (-10x + 2x2)) Combine like terms: -1x + -10x = -11x x = (5 + -11x + 2x2) Solving x = 5 + -11x + 2x2 Solving for variable 'x'. Reorder the terms: -5 + x + 11x + -2x2 = 5 + -11x + 2x2 + -5 + 11x + -2x2 Combine like terms: x + 11x = 12x -5 + 12x + -2x2 = 5 + -11x + 2x2 + -5 + 11x + -2x2 Reorder the terms: -5 + 12x + -2x2 = 5 + -5 + -11x + 11x + 2x2 + -2x2 Combine like terms: 5 + -5 = 0 -5 + 12x + -2x2 = 0 + -11x + 11x + 2x2 + -2x2 -5 + 12x + -2x2 = -11x + 11x + 2x2 + -2x2 Combine like terms: -11x + 11x = 0 -5 + 12x + -2x2 = 0 + 2x2 + -2x2 -5 + 12x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -5 + 12x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 2.5 + -6x + x2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + -6x + -2.5 + x2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + -6x + x2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + -6x + x2 = 0 + -2.5 -6x + x2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 -6x + x2 = -2.5 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = -2.5 + 9 Reorder the terms: 9 + -6x + x2 = -2.5 + 9 Combine like terms: -2.5 + 9 = 6.5 9 + -6x + x2 = 6.5 Factor a perfect square on the left side: (x + -3)(x + -3) = 6.5 Calculate the square root of the right side: 2.549509757 Break this problem into two subproblems by setting (x + -3) equal to 2.549509757 and -2.549509757.Subproblem 1
x + -3 = 2.549509757 Simplifying x + -3 = 2.549509757 Reorder the terms: -3 + x = 2.549509757 Solving -3 + x = 2.549509757 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 2.549509757 + 3 Combine like terms: -3 + 3 = 0 0 + x = 2.549509757 + 3 x = 2.549509757 + 3 Combine like terms: 2.549509757 + 3 = 5.549509757 x = 5.549509757 Simplifying x = 5.549509757Subproblem 2
x + -3 = -2.549509757 Simplifying x + -3 = -2.549509757 Reorder the terms: -3 + x = -2.549509757 Solving -3 + x = -2.549509757 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -2.549509757 + 3 Combine like terms: -3 + 3 = 0 0 + x = -2.549509757 + 3 x = -2.549509757 + 3 Combine like terms: -2.549509757 + 3 = 0.450490243 x = 0.450490243 Simplifying x = 0.450490243Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.549509757, 0.450490243}
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