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Simplifying 0.5x2 + x = 264 Reorder the terms: x + 0.5x2 = 264 Solving x + 0.5x2 = 264 Solving for variable 'x'. Reorder the terms: -264 + x + 0.5x2 = 264 + -264 Combine like terms: 264 + -264 = 0 -264 + x + 0.5x2 = 0 Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. -528 + 2x + x2 = 0 Move the constant term to the right: Add '528' to each side of the equation. -528 + 2x + 528 + x2 = 0 + 528 Reorder the terms: -528 + 528 + 2x + x2 = 0 + 528 Combine like terms: -528 + 528 = 0 0 + 2x + x2 = 0 + 528 2x + x2 = 0 + 528 Combine like terms: 0 + 528 = 528 2x + x2 = 528 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. 2x + 0.25 + x2 = 528 + 0.25 Reorder the terms: 0.25 + 2x + x2 = 528 + 0.25 Combine like terms: 528 + 0.25 = 528.25 0.25 + 2x + x2 = 528.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 528.25 Calculate the square root of the right side: 22.983689869 Break this problem into two subproblems by setting (x + 0.5) equal to 22.983689869 and -22.983689869.Subproblem 1
x + 0.5 = 22.983689869 Simplifying x + 0.5 = 22.983689869 Reorder the terms: 0.5 + x = 22.983689869 Solving 0.5 + x = 22.983689869 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 = 22.983689869 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 22.983689869 + -0.5 x = 22.983689869 + -0.5 Combine like terms: 22.983689869 + -0.5 = 22.483689869 x = 22.483689869 Simplifying x = 22.483689869Subproblem 2
x + 0.5 = -22.983689869 Simplifying x + 0.5 = -22.983689869 Reorder the terms: 0.5 + x = -22.983689869 Solving 0.5 + x = -22.983689869 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 = -22.983689869 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -22.983689869 + -0.5 x = -22.983689869 + -0.5 Combine like terms: -22.983689869 + -0.5 = -23.483689869 x = -23.483689869 Simplifying x = -23.483689869Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.483689869, -23.483689869}
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