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Simplifying (0.5 + -1x)(0.5 + -1x) = 4 Multiply (0.5 + -1x) * (0.5 + -1x) (0.5(0.5 + -1x) + -1x * (0.5 + -1x)) = 4 ((0.5 * 0.5 + -1x * 0.5) + -1x * (0.5 + -1x)) = 4 ((0.25 + -0.5x) + -1x * (0.5 + -1x)) = 4 (0.25 + -0.5x + (0.5 * -1x + -1x * -1x)) = 4 (0.25 + -0.5x + (-0.5x + 1x2)) = 4 Combine like terms: -0.5x + -0.5x = -1x (0.25 + -1x + 1x2) = 4 Solving 0.25 + -1x + 1x2 = 4 Solving for variable 'x'. Reorder the terms: 0.25 + -4 + -1x + 1x2 = 4 + -4 Combine like terms: 0.25 + -4 = -3.75 -3.75 + -1x + 1x2 = 4 + -4 Combine like terms: 4 + -4 = 0 -3.75 + -1x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '3.75' to each side of the equation. -3.75 + -1x + 3.75 + x2 = 0 + 3.75 Reorder the terms: -3.75 + 3.75 + -1x + x2 = 0 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + -1x + x2 = 0 + 3.75 -1x + x2 = 0 + 3.75 Combine like terms: 0 + 3.75 = 3.75 -1x + x2 = 3.75 The x term is -1x. 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. -1x + 0.25 + x2 = 3.75 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 3.75 + 0.25 Combine like terms: 3.75 + 0.25 = 4 0.25 + -1x + x2 = 4 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 4 Calculate the square root of the right side: 2 Break this problem into two subproblems by setting (x + -0.5) equal to 2 and -2.Subproblem 1
x + -0.5 = 2 Simplifying x + -0.5 = 2 Reorder the terms: -0.5 + x = 2 Solving -0.5 + x = 2 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 = 2 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 2 + 0.5 x = 2 + 0.5 Combine like terms: 2 + 0.5 = 2.5 x = 2.5 Simplifying x = 2.5Subproblem 2
x + -0.5 = -2 Simplifying x + -0.5 = -2 Reorder the terms: -0.5 + x = -2 Solving -0.5 + x = -2 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 = -2 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -2 + 0.5 x = -2 + 0.5 Combine like terms: -2 + 0.5 = -1.5 x = -1.5 Simplifying x = -1.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.5, -1.5}
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