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Simplifying x2 + 34x + 37 = 0 Reorder the terms: 37 + 34x + x2 = 0 Solving 37 + 34x + 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 + 34x + -37 + x2 = 0 + -37 Reorder the terms: 37 + -37 + 34x + x2 = 0 + -37 Combine like terms: 37 + -37 = 0 0 + 34x + x2 = 0 + -37 34x + x2 = 0 + -37 Combine like terms: 0 + -37 = -37 34x + x2 = -37 The x term is 34x. Take half its coefficient (17). Square it (289) and add it to both sides. Add '289' to each side of the equation. 34x + 289 + x2 = -37 + 289 Reorder the terms: 289 + 34x + x2 = -37 + 289 Combine like terms: -37 + 289 = 252 289 + 34x + x2 = 252 Factor a perfect square on the left side: (x + 17)(x + 17) = 252 Calculate the square root of the right side: 15.874507866 Break this problem into two subproblems by setting (x + 17) equal to 15.874507866 and -15.874507866.Subproblem 1
x + 17 = 15.874507866 Simplifying x + 17 = 15.874507866 Reorder the terms: 17 + x = 15.874507866 Solving 17 + x = 15.874507866 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-17' to each side of the equation. 17 + -17 + x = 15.874507866 + -17 Combine like terms: 17 + -17 = 0 0 + x = 15.874507866 + -17 x = 15.874507866 + -17 Combine like terms: 15.874507866 + -17 = -1.125492134 x = -1.125492134 Simplifying x = -1.125492134Subproblem 2
x + 17 = -15.874507866 Simplifying x + 17 = -15.874507866 Reorder the terms: 17 + x = -15.874507866 Solving 17 + x = -15.874507866 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-17' to each side of the equation. 17 + -17 + x = -15.874507866 + -17 Combine like terms: 17 + -17 = 0 0 + x = -15.874507866 + -17 x = -15.874507866 + -17 Combine like terms: -15.874507866 + -17 = -32.874507866 x = -32.874507866 Simplifying x = -32.874507866Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.125492134, -32.874507866}
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