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Simplifying 205x2 + -205x + 36 = 0 Reorder the terms: 36 + -205x + 205x2 = 0 Solving 36 + -205x + 205x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 205 the coefficient of the squared term: Divide each side by '205'. 0.1756097561 + -1x + x2 = 0 Move the constant term to the right: Add '-0.1756097561' to each side of the equation. 0.1756097561 + -1x + -0.1756097561 + x2 = 0 + -0.1756097561 Reorder the terms: 0.1756097561 + -0.1756097561 + -1x + x2 = 0 + -0.1756097561 Combine like terms: 0.1756097561 + -0.1756097561 = 0.0000000000 0.0000000000 + -1x + x2 = 0 + -0.1756097561 -1x + x2 = 0 + -0.1756097561 Combine like terms: 0 + -0.1756097561 = -0.1756097561 -1x + x2 = -0.1756097561 The x term is -1x. 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. -1x + 0.25 + x2 = -0.1756097561 + 0.25 Reorder the terms: 0.25 + -1x + x2 = -0.1756097561 + 0.25 Combine like terms: -0.1756097561 + 0.25 = 0.0743902439 0.25 + -1x + x2 = 0.0743902439 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 0.0743902439 Calculate the square root of the right side: 0.27274575 Break this problem into two subproblems by setting (x + -0.5) equal to 0.27274575 and -0.27274575.Subproblem 1
x + -0.5 = 0.27274575 Simplifying x + -0.5 = 0.27274575 Reorder the terms: -0.5 + x = 0.27274575 Solving -0.5 + x = 0.27274575 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 = 0.27274575 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 0.27274575 + 0.5 x = 0.27274575 + 0.5 Combine like terms: 0.27274575 + 0.5 = 0.77274575 x = 0.77274575 Simplifying x = 0.77274575Subproblem 2
x + -0.5 = -0.27274575 Simplifying x + -0.5 = -0.27274575 Reorder the terms: -0.5 + x = -0.27274575 Solving -0.5 + x = -0.27274575 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 = -0.27274575 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -0.27274575 + 0.5 x = -0.27274575 + 0.5 Combine like terms: -0.27274575 + 0.5 = 0.22725425 x = 0.22725425 Simplifying x = 0.22725425Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.77274575, 0.22725425}
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