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Simplifying (x + -2)(2x + 1) = 5 Reorder the terms: (-2 + x)(2x + 1) = 5 Reorder the terms: (-2 + x)(1 + 2x) = 5 Multiply (-2 + x) * (1 + 2x) (-2(1 + 2x) + x(1 + 2x)) = 5 ((1 * -2 + 2x * -2) + x(1 + 2x)) = 5 ((-2 + -4x) + x(1 + 2x)) = 5 (-2 + -4x + (1 * x + 2x * x)) = 5 (-2 + -4x + (1x + 2x2)) = 5 Combine like terms: -4x + 1x = -3x (-2 + -3x + 2x2) = 5 Solving -2 + -3x + 2x2 = 5 Solving for variable 'x'. Reorder the terms: -2 + -5 + -3x + 2x2 = 5 + -5 Combine like terms: -2 + -5 = -7 -7 + -3x + 2x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -7 + -3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -3.5 + -1.5x + x2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + -1.5x + 3.5 + x2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + -1.5x + x2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + -1.5x + x2 = 0 + 3.5 -1.5x + x2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 -1.5x + x2 = 3.5 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 = 3.5 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = 3.5 + 0.5625 Combine like terms: 3.5 + 0.5625 = 4.0625 0.5625 + -1.5x + x2 = 4.0625 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 4.0625 Calculate the square root of the right side: 2.015564437 Break this problem into two subproblems by setting (x + -0.75) equal to 2.015564437 and -2.015564437.Subproblem 1
x + -0.75 = 2.015564437 Simplifying x + -0.75 = 2.015564437 Reorder the terms: -0.75 + x = 2.015564437 Solving -0.75 + x = 2.015564437 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 = 2.015564437 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 2.015564437 + 0.75 x = 2.015564437 + 0.75 Combine like terms: 2.015564437 + 0.75 = 2.765564437 x = 2.765564437 Simplifying x = 2.765564437Subproblem 2
x + -0.75 = -2.015564437 Simplifying x + -0.75 = -2.015564437 Reorder the terms: -0.75 + x = -2.015564437 Solving -0.75 + x = -2.015564437 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 = -2.015564437 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -2.015564437 + 0.75 x = -2.015564437 + 0.75 Combine like terms: -2.015564437 + 0.75 = -1.265564437 x = -1.265564437 Simplifying x = -1.265564437Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.765564437, -1.265564437}
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