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Simplifying 0.5(x + -1)(x + -1) = 0 Reorder the terms: 0.5(-1 + x)(x + -1) = 0 Reorder the terms: 0.5(-1 + x)(-1 + x) = 0 Multiply (-1 + x) * (-1 + x) 0.5(-1(-1 + x) + x(-1 + x)) = 0 0.5((-1 * -1 + x * -1) + x(-1 + x)) = 0 0.5((1 + -1x) + x(-1 + x)) = 0 0.5(1 + -1x + (-1 * x + x * x)) = 0 0.5(1 + -1x + (-1x + x2)) = 0 Combine like terms: -1x + -1x = -2x 0.5(1 + -2x + x2) = 0 (1 * 0.5 + -2x * 0.5 + x2 * 0.5) = 0 (0.5 + -1x + 0.5x2) = 0 Solving 0.5 + -1x + 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'. 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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