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Simplifying x2 + 37x + 47 = 0 Reorder the terms: 47 + 37x + x2 = 0 Solving 47 + 37x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-47' to each side of the equation. 47 + 37x + -47 + x2 = 0 + -47 Reorder the terms: 47 + -47 + 37x + x2 = 0 + -47 Combine like terms: 47 + -47 = 0 0 + 37x + x2 = 0 + -47 37x + x2 = 0 + -47 Combine like terms: 0 + -47 = -47 37x + x2 = -47 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 = -47 + 342.25 Reorder the terms: 342.25 + 37x + x2 = -47 + 342.25 Combine like terms: -47 + 342.25 = 295.25 342.25 + 37x + x2 = 295.25 Factor a perfect square on the left side: (x + 18.5)(x + 18.5) = 295.25 Calculate the square root of the right side: 17.182840277 Break this problem into two subproblems by setting (x + 18.5) equal to 17.182840277 and -17.182840277.Subproblem 1
x + 18.5 = 17.182840277 Simplifying x + 18.5 = 17.182840277 Reorder the terms: 18.5 + x = 17.182840277 Solving 18.5 + x = 17.182840277 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 = 17.182840277 + -18.5 Combine like terms: 18.5 + -18.5 = 0.0 0.0 + x = 17.182840277 + -18.5 x = 17.182840277 + -18.5 Combine like terms: 17.182840277 + -18.5 = -1.317159723 x = -1.317159723 Simplifying x = -1.317159723Subproblem 2
x + 18.5 = -17.182840277 Simplifying x + 18.5 = -17.182840277 Reorder the terms: 18.5 + x = -17.182840277 Solving 18.5 + x = -17.182840277 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 = -17.182840277 + -18.5 Combine like terms: 18.5 + -18.5 = 0.0 0.0 + x = -17.182840277 + -18.5 x = -17.182840277 + -18.5 Combine like terms: -17.182840277 + -18.5 = -35.682840277 x = -35.682840277 Simplifying x = -35.682840277Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.317159723, -35.682840277}
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