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Simplifying 2(x + 0.5)(x + 0.5) = 0 Reorder the terms: 2(0.5 + x)(x + 0.5) = 0 Reorder the terms: 2(0.5 + x)(0.5 + x) = 0 Multiply (0.5 + x) * (0.5 + x) 2(0.5(0.5 + x) + x(0.5 + x)) = 0 2((0.5 * 0.5 + x * 0.5) + x(0.5 + x)) = 0 2((0.25 + 0.5x) + x(0.5 + x)) = 0 2(0.25 + 0.5x + (0.5 * x + x * x)) = 0 2(0.25 + 0.5x + (0.5x + x2)) = 0 Combine like terms: 0.5x + 0.5x = 1x 2(0.25 + 1x + x2) = 0 (0.25 * 2 + 1x * 2 + x2 * 2) = 0 (0.5 + 2x + 2x2) = 0 Solving 0.5 + 2x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 0.25 + x + x2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + x + -0.25 + x2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + x + x2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x + x2 = 0 + -0.25 x + x2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 x + x2 = -0.25 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 = -0.25 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = -0.25 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 1.25 + x2 = 0.00 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.00 Calculate the square root of the right side: 0.00 Break this problem into two subproblems by setting (x + 0.5) equal to 0.00 and 0.00.Subproblem 1
x + 0.5 = 0.00 Simplifying x + 0.5 = 0.00 Reorder the terms: 0.5 + x = 0.00 Solving 0.5 + x = 0.00 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 = 0.00 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.00 + -0.5 x = 0.00 + -0.5 Combine like terms: 0.00 + -0.5 = -0.5 x = -0.5 Simplifying x = -0.5Subproblem 2
x + 0.5 = 0.00 Simplifying x + 0.5 = 0.00 Reorder the terms: 0.5 + x = 0.00 Solving 0.5 + x = 0.00 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 = 0.00 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.00 + -0.5 x = 0.00 + -0.5 Combine like terms: 0.00 + -0.5 = -0.5 x = -0.5 Simplifying x = -0.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.5, -0.5}
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