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