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Simplifying x2 + 22x + 37 = 0 Reorder the terms: 37 + 22x + x2 = 0 Solving 37 + 22x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-37' to each side of the equation. 37 + 22x + -37 + x2 = 0 + -37 Reorder the terms: 37 + -37 + 22x + x2 = 0 + -37 Combine like terms: 37 + -37 = 0 0 + 22x + x2 = 0 + -37 22x + x2 = 0 + -37 Combine like terms: 0 + -37 = -37 22x + x2 = -37 The x term is 22x. Take half its coefficient (11). Square it (121) and add it to both sides. Add '121' to each side of the equation. 22x + 121 + x2 = -37 + 121 Reorder the terms: 121 + 22x + x2 = -37 + 121 Combine like terms: -37 + 121 = 84 121 + 22x + x2 = 84 Factor a perfect square on the left side: (x + 11)(x + 11) = 84 Calculate the square root of the right side: 9.16515139 Break this problem into two subproblems by setting (x + 11) equal to 9.16515139 and -9.16515139.Subproblem 1
x + 11 = 9.16515139 Simplifying x + 11 = 9.16515139 Reorder the terms: 11 + x = 9.16515139 Solving 11 + x = 9.16515139 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + x = 9.16515139 + -11 Combine like terms: 11 + -11 = 0 0 + x = 9.16515139 + -11 x = 9.16515139 + -11 Combine like terms: 9.16515139 + -11 = -1.83484861 x = -1.83484861 Simplifying x = -1.83484861Subproblem 2
x + 11 = -9.16515139 Simplifying x + 11 = -9.16515139 Reorder the terms: 11 + x = -9.16515139 Solving 11 + x = -9.16515139 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + x = -9.16515139 + -11 Combine like terms: 11 + -11 = 0 0 + x = -9.16515139 + -11 x = -9.16515139 + -11 Combine like terms: -9.16515139 + -11 = -20.16515139 x = -20.16515139 Simplifying x = -20.16515139Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.83484861, -20.16515139}
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