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Simplifying 0.7194x2 + 0.609x = 2.09635 Reorder the terms: 0.609x + 0.7194x2 = 2.09635 Solving 0.609x + 0.7194x2 = 2.09635 Solving for variable 'x'. Reorder the terms: -2.09635 + 0.609x + 0.7194x2 = 2.09635 + -2.09635 Combine like terms: 2.09635 + -2.09635 = 0.00000 -2.09635 + 0.609x + 0.7194x2 = 0.00000 Begin completing the square. Divide all terms by 0.7194 the coefficient of the squared term: Divide each side by '0.7194'. -2.914025577 + 0.8465387823x + x2 = 0.0 Move the constant term to the right: Add '2.914025577' to each side of the equation. -2.914025577 + 0.8465387823x + 2.914025577 + x2 = 0.0 + 2.914025577 Reorder the terms: -2.914025577 + 2.914025577 + 0.8465387823x + x2 = 0.0 + 2.914025577 Combine like terms: -2.914025577 + 2.914025577 = 0.000000000 0.000000000 + 0.8465387823x + x2 = 0.0 + 2.914025577 0.8465387823x + x2 = 0.0 + 2.914025577 Combine like terms: 0.0 + 2.914025577 = 2.914025577 0.8465387823x + x2 = 2.914025577 The x term is 0.8465387823x. Take half its coefficient (0.4232693912). Square it (0.1791569775) and add it to both sides. Add '0.1791569775' to each side of the equation. 0.8465387823x + 0.1791569775 + x2 = 2.914025577 + 0.1791569775 Reorder the terms: 0.1791569775 + 0.8465387823x + x2 = 2.914025577 + 0.1791569775 Combine like terms: 2.914025577 + 0.1791569775 = 3.0931825545 0.1791569775 + 0.8465387823x + x2 = 3.0931825545 Factor a perfect square on the left side: (x + 0.4232693912)(x + 0.4232693912) = 3.0931825545 Calculate the square root of the right side: 1.758744596 Break this problem into two subproblems by setting (x + 0.4232693912) equal to 1.758744596 and -1.758744596.Subproblem 1
x + 0.4232693912 = 1.758744596 Simplifying x + 0.4232693912 = 1.758744596 Reorder the terms: 0.4232693912 + x = 1.758744596 Solving 0.4232693912 + x = 1.758744596 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4232693912' to each side of the equation. 0.4232693912 + -0.4232693912 + x = 1.758744596 + -0.4232693912 Combine like terms: 0.4232693912 + -0.4232693912 = 0.0000000000 0.0000000000 + x = 1.758744596 + -0.4232693912 x = 1.758744596 + -0.4232693912 Combine like terms: 1.758744596 + -0.4232693912 = 1.3354752048 x = 1.3354752048 Simplifying x = 1.3354752048Subproblem 2
x + 0.4232693912 = -1.758744596 Simplifying x + 0.4232693912 = -1.758744596 Reorder the terms: 0.4232693912 + x = -1.758744596 Solving 0.4232693912 + x = -1.758744596 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4232693912' to each side of the equation. 0.4232693912 + -0.4232693912 + x = -1.758744596 + -0.4232693912 Combine like terms: 0.4232693912 + -0.4232693912 = 0.0000000000 0.0000000000 + x = -1.758744596 + -0.4232693912 x = -1.758744596 + -0.4232693912 Combine like terms: -1.758744596 + -0.4232693912 = -2.1820139872 x = -2.1820139872 Simplifying x = -2.1820139872Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.3354752048, -2.1820139872}
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