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Simplifying 7.25x2 + 3.38x = 4.68 Reorder the terms: 3.38x + 7.25x2 = 4.68 Solving 3.38x + 7.25x2 = 4.68 Solving for variable 'x'. Reorder the terms: -4.68 + 3.38x + 7.25x2 = 4.68 + -4.68 Combine like terms: 4.68 + -4.68 = 0.00 -4.68 + 3.38x + 7.25x2 = 0.00 Begin completing the square. Divide all terms by 7.25 the coefficient of the squared term: Divide each side by '7.25'. -0.6455172414 + 0.4662068966x + x2 = 0 Move the constant term to the right: Add '0.6455172414' to each side of the equation. -0.6455172414 + 0.4662068966x + 0.6455172414 + x2 = 0 + 0.6455172414 Reorder the terms: -0.6455172414 + 0.6455172414 + 0.4662068966x + x2 = 0 + 0.6455172414 Combine like terms: -0.6455172414 + 0.6455172414 = 0.0000000000 0.0000000000 + 0.4662068966x + x2 = 0 + 0.6455172414 0.4662068966x + x2 = 0 + 0.6455172414 Combine like terms: 0 + 0.6455172414 = 0.6455172414 0.4662068966x + x2 = 0.6455172414 The x term is 0.4662068966x. Take half its coefficient (0.2331034483). Square it (0.05433721761) and add it to both sides. Add '0.05433721761' to each side of the equation. 0.4662068966x + 0.05433721761 + x2 = 0.6455172414 + 0.05433721761 Reorder the terms: 0.05433721761 + 0.4662068966x + x2 = 0.6455172414 + 0.05433721761 Combine like terms: 0.6455172414 + 0.05433721761 = 0.69985445901 0.05433721761 + 0.4662068966x + x2 = 0.69985445901 Factor a perfect square on the left side: (x + 0.2331034483)(x + 0.2331034483) = 0.69985445901 Calculate the square root of the right side: 0.836573045 Break this problem into two subproblems by setting (x + 0.2331034483) equal to 0.836573045 and -0.836573045.Subproblem 1
x + 0.2331034483 = 0.836573045 Simplifying x + 0.2331034483 = 0.836573045 Reorder the terms: 0.2331034483 + x = 0.836573045 Solving 0.2331034483 + x = 0.836573045 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2331034483' to each side of the equation. 0.2331034483 + -0.2331034483 + x = 0.836573045 + -0.2331034483 Combine like terms: 0.2331034483 + -0.2331034483 = 0.0000000000 0.0000000000 + x = 0.836573045 + -0.2331034483 x = 0.836573045 + -0.2331034483 Combine like terms: 0.836573045 + -0.2331034483 = 0.6034695967 x = 0.6034695967 Simplifying x = 0.6034695967Subproblem 2
x + 0.2331034483 = -0.836573045 Simplifying x + 0.2331034483 = -0.836573045 Reorder the terms: 0.2331034483 + x = -0.836573045 Solving 0.2331034483 + x = -0.836573045 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2331034483' to each side of the equation. 0.2331034483 + -0.2331034483 + x = -0.836573045 + -0.2331034483 Combine like terms: 0.2331034483 + -0.2331034483 = 0.0000000000 0.0000000000 + x = -0.836573045 + -0.2331034483 x = -0.836573045 + -0.2331034483 Combine like terms: -0.836573045 + -0.2331034483 = -1.0696764933 x = -1.0696764933 Simplifying x = -1.0696764933Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6034695967, -1.0696764933}
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