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Simplifying x2 + 37x + 32 = 0 Reorder the terms: 32 + 37x + x2 = 0 Solving 32 + 37x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-32' to each side of the equation. 32 + 37x + -32 + x2 = 0 + -32 Reorder the terms: 32 + -32 + 37x + x2 = 0 + -32 Combine like terms: 32 + -32 = 0 0 + 37x + x2 = 0 + -32 37x + x2 = 0 + -32 Combine like terms: 0 + -32 = -32 37x + x2 = -32 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 = -32 + 342.25 Reorder the terms: 342.25 + 37x + x2 = -32 + 342.25 Combine like terms: -32 + 342.25 = 310.25 342.25 + 37x + x2 = 310.25 Factor a perfect square on the left side: (x + 18.5)(x + 18.5) = 310.25 Calculate the square root of the right side: 17.613914954 Break this problem into two subproblems by setting (x + 18.5) equal to 17.613914954 and -17.613914954.Subproblem 1
x + 18.5 = 17.613914954 Simplifying x + 18.5 = 17.613914954 Reorder the terms: 18.5 + x = 17.613914954 Solving 18.5 + x = 17.613914954 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 = 17.613914954 + -18.5 Combine like terms: 18.5 + -18.5 = 0.0 0.0 + x = 17.613914954 + -18.5 x = 17.613914954 + -18.5 Combine like terms: 17.613914954 + -18.5 = -0.886085046 x = -0.886085046 Simplifying x = -0.886085046Subproblem 2
x + 18.5 = -17.613914954 Simplifying x + 18.5 = -17.613914954 Reorder the terms: 18.5 + x = -17.613914954 Solving 18.5 + x = -17.613914954 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 = -17.613914954 + -18.5 Combine like terms: 18.5 + -18.5 = 0.0 0.0 + x = -17.613914954 + -18.5 x = -17.613914954 + -18.5 Combine like terms: -17.613914954 + -18.5 = -36.113914954 x = -36.113914954 Simplifying x = -36.113914954Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.886085046, -36.113914954}
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