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Simplifying 2x2 + x = 1.08 Reorder the terms: x + 2x2 = 1.08 Solving x + 2x2 = 1.08 Solving for variable 'x'. Reorder the terms: -1.08 + x + 2x2 = 1.08 + -1.08 Combine like terms: 1.08 + -1.08 = 0.00 -1.08 + x + 2x2 = 0.00 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -0.54 + 0.5x + x2 = 0.00 Move the constant term to the right: Add '0.54' to each side of the equation. -0.54 + 0.5x + 0.54 + x2 = 0.00 + 0.54 Reorder the terms: -0.54 + 0.54 + 0.5x + x2 = 0.00 + 0.54 Combine like terms: -0.54 + 0.54 = 0.00 0.00 + 0.5x + x2 = 0.00 + 0.54 0.5x + x2 = 0.00 + 0.54 Combine like terms: 0.00 + 0.54 = 0.54 0.5x + x2 = 0.54 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. 0.5x + 0.25 + x2 = 0.54 + 0.25 Reorder the terms: 0.25 + 0.5x + x2 = 0.54 + 0.25 Combine like terms: 0.54 + 0.25 = 0.79 0.25 + 0.5x + x2 = 0.79 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.79 Calculate the square root of the right side: 0.888819442 Break this problem into two subproblems by setting (x + 0.5) equal to 0.888819442 and -0.888819442.Subproblem 1
x + 0.5 = 0.888819442 Simplifying x + 0.5 = 0.888819442 Reorder the terms: 0.5 + x = 0.888819442 Solving 0.5 + x = 0.888819442 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 = 0.888819442 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.888819442 + -0.5 x = 0.888819442 + -0.5 Combine like terms: 0.888819442 + -0.5 = 0.388819442 x = 0.388819442 Simplifying x = 0.388819442Subproblem 2
x + 0.5 = -0.888819442 Simplifying x + 0.5 = -0.888819442 Reorder the terms: 0.5 + x = -0.888819442 Solving 0.5 + x = -0.888819442 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 = -0.888819442 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.888819442 + -0.5 x = -0.888819442 + -0.5 Combine like terms: -0.888819442 + -0.5 = -1.388819442 x = -1.388819442 Simplifying x = -1.388819442Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.388819442, -1.388819442}
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