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Simplifying (x + -1)(0.5x + 1) = 0 Reorder the terms: (-1 + x)(0.5x + 1) = 0 Reorder the terms: (-1 + x)(1 + 0.5x) = 0 Multiply (-1 + x) * (1 + 0.5x) (-1(1 + 0.5x) + x(1 + 0.5x)) = 0 ((1 * -1 + 0.5x * -1) + x(1 + 0.5x)) = 0 ((-1 + -0.5x) + x(1 + 0.5x)) = 0 (-1 + -0.5x + (1 * x + 0.5x * x)) = 0 (-1 + -0.5x + (1x + 0.5x2)) = 0 Combine like terms: -0.5x + 1x = 0.5x (-1 + 0.5x + 0.5x2) = 0 Solving -1 + 0.5x + 0.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. -2 + x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + x + x2 = 0 + 2 x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 x + x2 = 2 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 2 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 2 + 0.25 Combine like terms: 2 + 0.25 = 2.25 1.25 + x2 = 2.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 2.25 Calculate the square root of the right side: 1.5 Break this problem into two subproblems by setting (x + 0.5) equal to 1.5 and -1.5.Subproblem 1
x + 0.5 = 1.5 Simplifying x + 0.5 = 1.5 Reorder the terms: 0.5 + x = 1.5 Solving 0.5 + x = 1.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 1.5 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.5 + -0.5 x = 1.5 + -0.5 Combine like terms: 1.5 + -0.5 = 1 x = 1 Simplifying x = 1Subproblem 2
x + 0.5 = -1.5 Simplifying x + 0.5 = -1.5 Reorder the terms: 0.5 + x = -1.5 Solving 0.5 + x = -1.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -1.5 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.5 + -0.5 x = -1.5 + -0.5 Combine like terms: -1.5 + -0.5 = -2 x = -2 Simplifying x = -2Solution
The solution to the problem is based on the solutions from the subproblems. x = {1, -2}
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