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Simplifying x2 + -23x + 82 = 0 Reorder the terms: 82 + -23x + x2 = 0 Solving 82 + -23x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-82' to each side of the equation. 82 + -23x + -82 + x2 = 0 + -82 Reorder the terms: 82 + -82 + -23x + x2 = 0 + -82 Combine like terms: 82 + -82 = 0 0 + -23x + x2 = 0 + -82 -23x + x2 = 0 + -82 Combine like terms: 0 + -82 = -82 -23x + x2 = -82 The x term is -23x. Take half its coefficient (-11.5). Square it (132.25) and add it to both sides. Add '132.25' to each side of the equation. -23x + 132.25 + x2 = -82 + 132.25 Reorder the terms: 132.25 + -23x + x2 = -82 + 132.25 Combine like terms: -82 + 132.25 = 50.25 132.25 + -23x + x2 = 50.25 Factor a perfect square on the left side: (x + -11.5)(x + -11.5) = 50.25 Calculate the square root of the right side: 7.088723439 Break this problem into two subproblems by setting (x + -11.5) equal to 7.088723439 and -7.088723439.Subproblem 1
x + -11.5 = 7.088723439 Simplifying x + -11.5 = 7.088723439 Reorder the terms: -11.5 + x = 7.088723439 Solving -11.5 + x = 7.088723439 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.5' to each side of the equation. -11.5 + 11.5 + x = 7.088723439 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + x = 7.088723439 + 11.5 x = 7.088723439 + 11.5 Combine like terms: 7.088723439 + 11.5 = 18.588723439 x = 18.588723439 Simplifying x = 18.588723439Subproblem 2
x + -11.5 = -7.088723439 Simplifying x + -11.5 = -7.088723439 Reorder the terms: -11.5 + x = -7.088723439 Solving -11.5 + x = -7.088723439 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.5' to each side of the equation. -11.5 + 11.5 + x = -7.088723439 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + x = -7.088723439 + 11.5 x = -7.088723439 + 11.5 Combine like terms: -7.088723439 + 11.5 = 4.411276561 x = 4.411276561 Simplifying x = 4.411276561Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.588723439, 4.411276561}
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