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Simplifying 3.25 = -0.5x2 + x + 6 Reorder the terms: 3.25 = 6 + x + -0.5x2 Solving 3.25 = 6 + x + -0.5x2 Solving for variable 'x'. Combine like terms: 3.25 + -6 = -2.75 -2.75 + -1x + 0.5x2 = 6 + x + -0.5x2 + -6 + -1x + 0.5x2 Reorder the terms: -2.75 + -1x + 0.5x2 = 6 + -6 + x + -1x + -0.5x2 + 0.5x2 Combine like terms: 6 + -6 = 0 -2.75 + -1x + 0.5x2 = 0 + x + -1x + -0.5x2 + 0.5x2 -2.75 + -1x + 0.5x2 = x + -1x + -0.5x2 + 0.5x2 Combine like terms: x + -1x = 0 -2.75 + -1x + 0.5x2 = 0 + -0.5x2 + 0.5x2 -2.75 + -1x + 0.5x2 = -0.5x2 + 0.5x2 Combine like terms: -0.5x2 + 0.5x2 = 0.0 -2.75 + -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'. -5.5 + -2x + x2 = 0 Move the constant term to the right: Add '5.5' to each side of the equation. -5.5 + -2x + 5.5 + x2 = 0 + 5.5 Reorder the terms: -5.5 + 5.5 + -2x + x2 = 0 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + -2x + x2 = 0 + 5.5 -2x + x2 = 0 + 5.5 Combine like terms: 0 + 5.5 = 5.5 -2x + x2 = 5.5 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 = 5.5 + 1 Reorder the terms: 1 + -2x + x2 = 5.5 + 1 Combine like terms: 5.5 + 1 = 6.5 1 + -2x + x2 = 6.5 Factor a perfect square on the left side: (x + -1)(x + -1) = 6.5 Calculate the square root of the right side: 2.549509757 Break this problem into two subproblems by setting (x + -1) equal to 2.549509757 and -2.549509757.Subproblem 1
x + -1 = 2.549509757 Simplifying x + -1 = 2.549509757 Reorder the terms: -1 + x = 2.549509757 Solving -1 + x = 2.549509757 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 = 2.549509757 + 1 Combine like terms: -1 + 1 = 0 0 + x = 2.549509757 + 1 x = 2.549509757 + 1 Combine like terms: 2.549509757 + 1 = 3.549509757 x = 3.549509757 Simplifying x = 3.549509757Subproblem 2
x + -1 = -2.549509757 Simplifying x + -1 = -2.549509757 Reorder the terms: -1 + x = -2.549509757 Solving -1 + x = -2.549509757 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 = -2.549509757 + 1 Combine like terms: -1 + 1 = 0 0 + x = -2.549509757 + 1 x = -2.549509757 + 1 Combine like terms: -2.549509757 + 1 = -1.549509757 x = -1.549509757 Simplifying x = -1.549509757Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.549509757, -1.549509757}
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