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Simplifying (2x + 1)(x + -1) = 36 Reorder the terms: (1 + 2x)(x + -1) = 36 Reorder the terms: (1 + 2x)(-1 + x) = 36 Multiply (1 + 2x) * (-1 + x) (1(-1 + x) + 2x * (-1 + x)) = 36 ((-1 * 1 + x * 1) + 2x * (-1 + x)) = 36 ((-1 + 1x) + 2x * (-1 + x)) = 36 (-1 + 1x + (-1 * 2x + x * 2x)) = 36 (-1 + 1x + (-2x + 2x2)) = 36 Combine like terms: 1x + -2x = -1x (-1 + -1x + 2x2) = 36 Solving -1 + -1x + 2x2 = 36 Solving for variable 'x'. Reorder the terms: -1 + -36 + -1x + 2x2 = 36 + -36 Combine like terms: -1 + -36 = -37 -37 + -1x + 2x2 = 36 + -36 Combine like terms: 36 + -36 = 0 -37 + -1x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -18.5 + -0.5x + x2 = 0 Move the constant term to the right: Add '18.5' to each side of the equation. -18.5 + -0.5x + 18.5 + x2 = 0 + 18.5 Reorder the terms: -18.5 + 18.5 + -0.5x + x2 = 0 + 18.5 Combine like terms: -18.5 + 18.5 = 0.0 0.0 + -0.5x + x2 = 0 + 18.5 -0.5x + x2 = 0 + 18.5 Combine like terms: 0 + 18.5 = 18.5 -0.5x + x2 = 18.5 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = 18.5 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 18.5 + 0.0625 Combine like terms: 18.5 + 0.0625 = 18.5625 0.0625 + -0.5x + x2 = 18.5625 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 18.5625 Calculate the square root of the right side: 4.308421985 Break this problem into two subproblems by setting (x + -0.25) equal to 4.308421985 and -4.308421985.Subproblem 1
x + -0.25 = 4.308421985 Simplifying x + -0.25 = 4.308421985 Reorder the terms: -0.25 + x = 4.308421985 Solving -0.25 + x = 4.308421985 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 4.308421985 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 4.308421985 + 0.25 x = 4.308421985 + 0.25 Combine like terms: 4.308421985 + 0.25 = 4.558421985 x = 4.558421985 Simplifying x = 4.558421985Subproblem 2
x + -0.25 = -4.308421985 Simplifying x + -0.25 = -4.308421985 Reorder the terms: -0.25 + x = -4.308421985 Solving -0.25 + x = -4.308421985 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -4.308421985 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -4.308421985 + 0.25 x = -4.308421985 + 0.25 Combine like terms: -4.308421985 + 0.25 = -4.058421985 x = -4.058421985 Simplifying x = -4.058421985Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.558421985, -4.058421985}
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