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Simplifying x2 + 37x + 29 = 0 Reorder the terms: 29 + 37x + x2 = 0 Solving 29 + 37x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-29' to each side of the equation. 29 + 37x + -29 + x2 = 0 + -29 Reorder the terms: 29 + -29 + 37x + x2 = 0 + -29 Combine like terms: 29 + -29 = 0 0 + 37x + x2 = 0 + -29 37x + x2 = 0 + -29 Combine like terms: 0 + -29 = -29 37x + x2 = -29 The x term is 37x. Take half its coefficient (18.5). Square it (342.25) and add it to both sides. Add '342.25' to each side of the equation. 37x + 342.25 + x2 = -29 + 342.25 Reorder the terms: 342.25 + 37x + x2 = -29 + 342.25 Combine like terms: -29 + 342.25 = 313.25 342.25 + 37x + x2 = 313.25 Factor a perfect square on the left side: (x + 18.5)(x + 18.5) = 313.25 Calculate the square root of the right side: 17.69887002 Break this problem into two subproblems by setting (x + 18.5) equal to 17.69887002 and -17.69887002.Subproblem 1
x + 18.5 = 17.69887002 Simplifying x + 18.5 = 17.69887002 Reorder the terms: 18.5 + x = 17.69887002 Solving 18.5 + x = 17.69887002 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18.5' to each side of the equation. 18.5 + -18.5 + x = 17.69887002 + -18.5 Combine like terms: 18.5 + -18.5 = 0.0 0.0 + x = 17.69887002 + -18.5 x = 17.69887002 + -18.5 Combine like terms: 17.69887002 + -18.5 = -0.80112998 x = -0.80112998 Simplifying x = -0.80112998Subproblem 2
x + 18.5 = -17.69887002 Simplifying x + 18.5 = -17.69887002 Reorder the terms: 18.5 + x = -17.69887002 Solving 18.5 + x = -17.69887002 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18.5' to each side of the equation. 18.5 + -18.5 + x = -17.69887002 + -18.5 Combine like terms: 18.5 + -18.5 = 0.0 0.0 + x = -17.69887002 + -18.5 x = -17.69887002 + -18.5 Combine like terms: -17.69887002 + -18.5 = -36.19887002 x = -36.19887002 Simplifying x = -36.19887002Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.80112998, -36.19887002}
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