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Simplifying 0.941x2 + 564.7x + -265200 = 0 Reorder the terms: -265200 + 564.7x + 0.941x2 = 0 Solving -265200 + 564.7x + 0.941x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.941 the coefficient of the squared term: Divide each side by '0.941'. -281827.8427 + 600.1062699x + x2 = 0 Move the constant term to the right: Add '281827.8427' to each side of the equation. -281827.8427 + 600.1062699x + 281827.8427 + x2 = 0 + 281827.8427 Reorder the terms: -281827.8427 + 281827.8427 + 600.1062699x + x2 = 0 + 281827.8427 Combine like terms: -281827.8427 + 281827.8427 = 0.0000 0.0000 + 600.1062699x + x2 = 0 + 281827.8427 600.1062699x + x2 = 0 + 281827.8427 Combine like terms: 0 + 281827.8427 = 281827.8427 600.1062699x + x2 = 281827.8427 The x term is 600.1062699x. Take half its coefficient (300.053135). Square it (90031.88382) and add it to both sides. Add '90031.88382' to each side of the equation. 600.1062699x + 90031.88382 + x2 = 281827.8427 + 90031.88382 Reorder the terms: 90031.88382 + 600.1062699x + x2 = 281827.8427 + 90031.88382 Combine like terms: 281827.8427 + 90031.88382 = 371859.72652 90031.88382 + 600.1062699x + x2 = 371859.72652 Factor a perfect square on the left side: (x + 300.053135)(x + 300.053135) = 371859.72652 Calculate the square root of the right side: 609.803022721 Break this problem into two subproblems by setting (x + 300.053135) equal to 609.803022721 and -609.803022721.Subproblem 1
x + 300.053135 = 609.803022721 Simplifying x + 300.053135 = 609.803022721 Reorder the terms: 300.053135 + x = 609.803022721 Solving 300.053135 + x = 609.803022721 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-300.053135' to each side of the equation. 300.053135 + -300.053135 + x = 609.803022721 + -300.053135 Combine like terms: 300.053135 + -300.053135 = 0.000000 0.000000 + x = 609.803022721 + -300.053135 x = 609.803022721 + -300.053135 Combine like terms: 609.803022721 + -300.053135 = 309.749887721 x = 309.749887721 Simplifying x = 309.749887721Subproblem 2
x + 300.053135 = -609.803022721 Simplifying x + 300.053135 = -609.803022721 Reorder the terms: 300.053135 + x = -609.803022721 Solving 300.053135 + x = -609.803022721 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-300.053135' to each side of the equation. 300.053135 + -300.053135 + x = -609.803022721 + -300.053135 Combine like terms: 300.053135 + -300.053135 = 0.000000 0.000000 + x = -609.803022721 + -300.053135 x = -609.803022721 + -300.053135 Combine like terms: -609.803022721 + -300.053135 = -909.856157721 x = -909.856157721 Simplifying x = -909.856157721Solution
The solution to the problem is based on the solutions from the subproblems. x = {309.749887721, -909.856157721}
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