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Simplifying 0.5x2 + -5.5x + 12 = 0 Reorder the terms: 12 + -5.5x + 0.5x2 = 0 Solving 12 + -5.5x + 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'. 24 + -11x + x2 = 0 Move the constant term to the right: Add '-24' to each side of the equation. 24 + -11x + -24 + x2 = 0 + -24 Reorder the terms: 24 + -24 + -11x + x2 = 0 + -24 Combine like terms: 24 + -24 = 0 0 + -11x + x2 = 0 + -24 -11x + x2 = 0 + -24 Combine like terms: 0 + -24 = -24 -11x + x2 = -24 The x term is -11x. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11x + 30.25 + x2 = -24 + 30.25 Reorder the terms: 30.25 + -11x + x2 = -24 + 30.25 Combine like terms: -24 + 30.25 = 6.25 30.25 + -11x + x2 = 6.25 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 6.25 Calculate the square root of the right side: 2.5 Break this problem into two subproblems by setting (x + -5.5) equal to 2.5 and -2.5.Subproblem 1
x + -5.5 = 2.5 Simplifying x + -5.5 = 2.5 Reorder the terms: -5.5 + x = 2.5 Solving -5.5 + x = 2.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = 2.5 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 2.5 + 5.5 x = 2.5 + 5.5 Combine like terms: 2.5 + 5.5 = 8 x = 8 Simplifying x = 8Subproblem 2
x + -5.5 = -2.5 Simplifying x + -5.5 = -2.5 Reorder the terms: -5.5 + x = -2.5 Solving -5.5 + x = -2.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = -2.5 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -2.5 + 5.5 x = -2.5 + 5.5 Combine like terms: -2.5 + 5.5 = 3 x = 3 Simplifying x = 3Solution
The solution to the problem is based on the solutions from the subproblems. x = {8, 3}
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