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Simplifying 3.5 = -2x2 + -2x + 3 Reorder the terms: 3.5 = 3 + -2x + -2x2 Solving 3.5 = 3 + -2x + -2x2 Solving for variable 'x'. Combine like terms: 3.5 + -3 = 0.5 0.5 + 2x + 2x2 = 3 + -2x + -2x2 + -3 + 2x + 2x2 Reorder the terms: 0.5 + 2x + 2x2 = 3 + -3 + -2x + 2x + -2x2 + 2x2 Combine like terms: 3 + -3 = 0 0.5 + 2x + 2x2 = 0 + -2x + 2x + -2x2 + 2x2 0.5 + 2x + 2x2 = -2x + 2x + -2x2 + 2x2 Combine like terms: -2x + 2x = 0 0.5 + 2x + 2x2 = 0 + -2x2 + 2x2 0.5 + 2x + 2x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 0.5 + 2x + 2x2 = 0 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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