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Simplifying (2x + 1)(x + -5) = (2x + -1) + -1(x + -1) Reorder the terms: (1 + 2x)(x + -5) = (2x + -1) + -1(x + -1) Reorder the terms: (1 + 2x)(-5 + x) = (2x + -1) + -1(x + -1) Multiply (1 + 2x) * (-5 + x) (1(-5 + x) + 2x * (-5 + x)) = (2x + -1) + -1(x + -1) ((-5 * 1 + x * 1) + 2x * (-5 + x)) = (2x + -1) + -1(x + -1) ((-5 + 1x) + 2x * (-5 + x)) = (2x + -1) + -1(x + -1) (-5 + 1x + (-5 * 2x + x * 2x)) = (2x + -1) + -1(x + -1) (-5 + 1x + (-10x + 2x2)) = (2x + -1) + -1(x + -1) Combine like terms: 1x + -10x = -9x (-5 + -9x + 2x2) = (2x + -1) + -1(x + -1) Reorder the terms: -5 + -9x + 2x2 = (-1 + 2x) + -1(x + -1) Remove parenthesis around (-1 + 2x) -5 + -9x + 2x2 = -1 + 2x + -1(x + -1) Reorder the terms: -5 + -9x + 2x2 = -1 + 2x + -1(-1 + x) -5 + -9x + 2x2 = -1 + 2x + (-1 * -1 + x * -1) -5 + -9x + 2x2 = -1 + 2x + (1 + -1x) Reorder the terms: -5 + -9x + 2x2 = -1 + 1 + 2x + -1x Combine like terms: -1 + 1 = 0 -5 + -9x + 2x2 = 0 + 2x + -1x -5 + -9x + 2x2 = 2x + -1x Combine like terms: 2x + -1x = 1x -5 + -9x + 2x2 = 1x Solving -5 + -9x + 2x2 = 1x Solving for variable 'x'. Reorder the terms: -5 + -9x + -1x + 2x2 = 1x + -1x Combine like terms: -9x + -1x = -10x -5 + -10x + 2x2 = 1x + -1x Combine like terms: 1x + -1x = 0 -5 + -10x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -2.5 + -5x + x2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + -5x + 2.5 + x2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + -5x + x2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + -5x + x2 = 0 + 2.5 -5x + x2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 -5x + x2 = 2.5 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 2.5 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 2.5 + 6.25 Combine like terms: 2.5 + 6.25 = 8.75 6.25 + -5x + x2 = 8.75 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 8.75 Calculate the square root of the right side: 2.958039892 Break this problem into two subproblems by setting (x + -2.5) equal to 2.958039892 and -2.958039892.Subproblem 1
x + -2.5 = 2.958039892 Simplifying x + -2.5 = 2.958039892 Reorder the terms: -2.5 + x = 2.958039892 Solving -2.5 + x = 2.958039892 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 2.958039892 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 2.958039892 + 2.5 x = 2.958039892 + 2.5 Combine like terms: 2.958039892 + 2.5 = 5.458039892 x = 5.458039892 Simplifying x = 5.458039892Subproblem 2
x + -2.5 = -2.958039892 Simplifying x + -2.5 = -2.958039892 Reorder the terms: -2.5 + x = -2.958039892 Solving -2.5 + x = -2.958039892 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -2.958039892 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -2.958039892 + 2.5 x = -2.958039892 + 2.5 Combine like terms: -2.958039892 + 2.5 = -0.458039892 x = -0.458039892 Simplifying x = -0.458039892Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.458039892, -0.458039892}
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