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Simplifying (2x + 5)(x + -1) = -1 Reorder the terms: (5 + 2x)(x + -1) = -1 Reorder the terms: (5 + 2x)(-1 + x) = -1 Multiply (5 + 2x) * (-1 + x) (5(-1 + x) + 2x * (-1 + x)) = -1 ((-1 * 5 + x * 5) + 2x * (-1 + x)) = -1 ((-5 + 5x) + 2x * (-1 + x)) = -1 (-5 + 5x + (-1 * 2x + x * 2x)) = -1 (-5 + 5x + (-2x + 2x2)) = -1 Combine like terms: 5x + -2x = 3x (-5 + 3x + 2x2) = -1 Solving -5 + 3x + 2x2 = -1 Solving for variable 'x'. Reorder the terms: -5 + 1 + 3x + 2x2 = -1 + 1 Combine like terms: -5 + 1 = -4 -4 + 3x + 2x2 = -1 + 1 Combine like terms: -1 + 1 = 0 -4 + 3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -2 + 1.5x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 1.5x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + 1.5x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 1.5x + x2 = 0 + 2 1.5x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 1.5x + x2 = 2 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = 2 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 2 + 0.5625 Combine like terms: 2 + 0.5625 = 2.5625 0.5625 + 1.5x + x2 = 2.5625 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 2.5625 Calculate the square root of the right side: 1.600781059 Break this problem into two subproblems by setting (x + 0.75) equal to 1.600781059 and -1.600781059.Subproblem 1
x + 0.75 = 1.600781059 Simplifying x + 0.75 = 1.600781059 Reorder the terms: 0.75 + x = 1.600781059 Solving 0.75 + x = 1.600781059 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 1.600781059 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 1.600781059 + -0.75 x = 1.600781059 + -0.75 Combine like terms: 1.600781059 + -0.75 = 0.850781059 x = 0.850781059 Simplifying x = 0.850781059Subproblem 2
x + 0.75 = -1.600781059 Simplifying x + 0.75 = -1.600781059 Reorder the terms: 0.75 + x = -1.600781059 Solving 0.75 + x = -1.600781059 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -1.600781059 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -1.600781059 + -0.75 x = -1.600781059 + -0.75 Combine like terms: -1.600781059 + -0.75 = -2.350781059 x = -2.350781059 Simplifying x = -2.350781059Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.850781059, -2.350781059}
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