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Simplifying 0.5x2 + -1.5x + 1 = 0 Reorder the terms: 1 + -1.5x + 0.5x2 = 0 Solving 1 + -1.5x + 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'. 2 + -3x + x2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -3x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + -3x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3x + x2 = 0 + -2 -3x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 -3x + x2 = -2 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = -2 + 2.25 Reorder the terms: 2.25 + -3x + x2 = -2 + 2.25 Combine like terms: -2 + 2.25 = 0.25 2.25 + -3x + x2 = 0.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 0.25 Calculate the square root of the right side: 0.5 Break this problem into two subproblems by setting (x + -1.5) equal to 0.5 and -0.5.Subproblem 1
x + -1.5 = 0.5 Simplifying x + -1.5 = 0.5 Reorder the terms: -1.5 + x = 0.5 Solving -1.5 + x = 0.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 0.5 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 0.5 + 1.5 x = 0.5 + 1.5 Combine like terms: 0.5 + 1.5 = 2 x = 2 Simplifying x = 2Subproblem 2
x + -1.5 = -0.5 Simplifying x + -1.5 = -0.5 Reorder the terms: -1.5 + x = -0.5 Solving -1.5 + x = -0.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -0.5 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -0.5 + 1.5 x = -0.5 + 1.5 Combine like terms: -0.5 + 1.5 = 1 x = 1 Simplifying x = 1Solution
The solution to the problem is based on the solutions from the subproblems. x = {2, 1}
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