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Simplifying 0.5 = -0.5x2 + 1x + 2 Reorder the terms: 0.5 = 2 + 1x + -0.5x2 Solving 0.5 = 2 + 1x + -0.5x2 Solving for variable 'x'. Combine like terms: 0.5 + -2 = -1.5 -1.5 + -1x + 0.5x2 = 2 + 1x + -0.5x2 + -2 + -1x + 0.5x2 Reorder the terms: -1.5 + -1x + 0.5x2 = 2 + -2 + 1x + -1x + -0.5x2 + 0.5x2 Combine like terms: 2 + -2 = 0 -1.5 + -1x + 0.5x2 = 0 + 1x + -1x + -0.5x2 + 0.5x2 -1.5 + -1x + 0.5x2 = 1x + -1x + -0.5x2 + 0.5x2 Combine like terms: 1x + -1x = 0 -1.5 + -1x + 0.5x2 = 0 + -0.5x2 + 0.5x2 -1.5 + -1x + 0.5x2 = -0.5x2 + 0.5x2 Combine like terms: -0.5x2 + 0.5x2 = 0.0 -1.5 + -1x + 0.5x2 = 0.0 Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. -3 + -2x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -2x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + -2x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -2x + x2 = 0 + 3 -2x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 -2x + x2 = 3 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 = 3 + 1 Reorder the terms: 1 + -2x + x2 = 3 + 1 Combine like terms: 3 + 1 = 4 1 + -2x + x2 = 4 Factor a perfect square on the left side: (x + -1)(x + -1) = 4 Calculate the square root of the right side: 2 Break this problem into two subproblems by setting (x + -1) equal to 2 and -2.Subproblem 1
x + -1 = 2 Simplifying x + -1 = 2 Reorder the terms: -1 + x = 2 Solving -1 + x = 2 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 = 2 + 1 Combine like terms: -1 + 1 = 0 0 + x = 2 + 1 x = 2 + 1 Combine like terms: 2 + 1 = 3 x = 3 Simplifying x = 3Subproblem 2
x + -1 = -2 Simplifying x + -1 = -2 Reorder the terms: -1 + x = -2 Solving -1 + x = -2 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 = -2 + 1 Combine like terms: -1 + 1 = 0 0 + x = -2 + 1 x = -2 + 1 Combine like terms: -2 + 1 = -1 x = -1 Simplifying x = -1Solution
The solution to the problem is based on the solutions from the subproblems. x = {3, -1}
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