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Simplifying (x + -1)(x + -0.5) = 0 Reorder the terms: (-1 + x)(x + -0.5) = 0 Reorder the terms: (-1 + x)(-0.5 + x) = 0 Multiply (-1 + x) * (-0.5 + x) (-1(-0.5 + x) + x(-0.5 + x)) = 0 ((-0.5 * -1 + x * -1) + x(-0.5 + x)) = 0 ((0.5 + -1x) + x(-0.5 + x)) = 0 (0.5 + -1x + (-0.5 * x + x * x)) = 0 (0.5 + -1x + (-0.5x + x2)) = 0 Combine like terms: -1x + -0.5x = -1.5x (0.5 + -1.5x + x2) = 0 Solving 0.5 + -1.5x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + -1.5x + -0.5 + x2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + -1.5x + x2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + -1.5x + x2 = 0 + -0.5 -1.5x + x2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 -1.5x + x2 = -0.5 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 = -0.5 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = -0.5 + 0.5625 Combine like terms: -0.5 + 0.5625 = 0.0625 0.5625 + -1.5x + x2 = 0.0625 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 0.0625 Calculate the square root of the right side: 0.25 Break this problem into two subproblems by setting (x + -0.75) equal to 0.25 and -0.25.Subproblem 1
x + -0.75 = 0.25 Simplifying x + -0.75 = 0.25 Reorder the terms: -0.75 + x = 0.25 Solving -0.75 + x = 0.25 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 = 0.25 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 0.25 + 0.75 x = 0.25 + 0.75 Combine like terms: 0.25 + 0.75 = 1 x = 1 Simplifying x = 1Subproblem 2
x + -0.75 = -0.25 Simplifying x + -0.75 = -0.25 Reorder the terms: -0.75 + x = -0.25 Solving -0.75 + x = -0.25 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 = -0.25 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -0.25 + 0.75 x = -0.25 + 0.75 Combine like terms: -0.25 + 0.75 = 0.5 x = 0.5 Simplifying x = 0.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {1, 0.5}
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