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Simplifying (x + -1)(2x + -1) = 33 Reorder the terms: (-1 + x)(2x + -1) = 33 Reorder the terms: (-1 + x)(-1 + 2x) = 33 Multiply (-1 + x) * (-1 + 2x) (-1(-1 + 2x) + x(-1 + 2x)) = 33 ((-1 * -1 + 2x * -1) + x(-1 + 2x)) = 33 ((1 + -2x) + x(-1 + 2x)) = 33 (1 + -2x + (-1 * x + 2x * x)) = 33 (1 + -2x + (-1x + 2x2)) = 33 Combine like terms: -2x + -1x = -3x (1 + -3x + 2x2) = 33 Solving 1 + -3x + 2x2 = 33 Solving for variable 'x'. Reorder the terms: 1 + -33 + -3x + 2x2 = 33 + -33 Combine like terms: 1 + -33 = -32 -32 + -3x + 2x2 = 33 + -33 Combine like terms: 33 + -33 = 0 -32 + -3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -16 + -1.5x + x2 = 0 Move the constant term to the right: Add '16' to each side of the equation. -16 + -1.5x + 16 + x2 = 0 + 16 Reorder the terms: -16 + 16 + -1.5x + x2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + -1.5x + x2 = 0 + 16 -1.5x + x2 = 0 + 16 Combine like terms: 0 + 16 = 16 -1.5x + x2 = 16 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 = 16 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = 16 + 0.5625 Combine like terms: 16 + 0.5625 = 16.5625 0.5625 + -1.5x + x2 = 16.5625 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 16.5625 Calculate the square root of the right side: 4.069705149 Break this problem into two subproblems by setting (x + -0.75) equal to 4.069705149 and -4.069705149.Subproblem 1
x + -0.75 = 4.069705149 Simplifying x + -0.75 = 4.069705149 Reorder the terms: -0.75 + x = 4.069705149 Solving -0.75 + x = 4.069705149 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 = 4.069705149 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 4.069705149 + 0.75 x = 4.069705149 + 0.75 Combine like terms: 4.069705149 + 0.75 = 4.819705149 x = 4.819705149 Simplifying x = 4.819705149Subproblem 2
x + -0.75 = -4.069705149 Simplifying x + -0.75 = -4.069705149 Reorder the terms: -0.75 + x = -4.069705149 Solving -0.75 + x = -4.069705149 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 = -4.069705149 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -4.069705149 + 0.75 x = -4.069705149 + 0.75 Combine like terms: -4.069705149 + 0.75 = -3.319705149 x = -3.319705149 Simplifying x = -3.319705149Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.819705149, -3.319705149}
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