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Simplifying x2 + 36x + 43 = 0 Reorder the terms: 43 + 36x + x2 = 0 Solving 43 + 36x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-43' to each side of the equation. 43 + 36x + -43 + x2 = 0 + -43 Reorder the terms: 43 + -43 + 36x + x2 = 0 + -43 Combine like terms: 43 + -43 = 0 0 + 36x + x2 = 0 + -43 36x + x2 = 0 + -43 Combine like terms: 0 + -43 = -43 36x + x2 = -43 The x term is 36x. Take half its coefficient (18). Square it (324) and add it to both sides. Add '324' to each side of the equation. 36x + 324 + x2 = -43 + 324 Reorder the terms: 324 + 36x + x2 = -43 + 324 Combine like terms: -43 + 324 = 281 324 + 36x + x2 = 281 Factor a perfect square on the left side: (x + 18)(x + 18) = 281 Calculate the square root of the right side: 16.763054614 Break this problem into two subproblems by setting (x + 18) equal to 16.763054614 and -16.763054614.Subproblem 1
x + 18 = 16.763054614 Simplifying x + 18 = 16.763054614 Reorder the terms: 18 + x = 16.763054614 Solving 18 + x = 16.763054614 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18' to each side of the equation. 18 + -18 + x = 16.763054614 + -18 Combine like terms: 18 + -18 = 0 0 + x = 16.763054614 + -18 x = 16.763054614 + -18 Combine like terms: 16.763054614 + -18 = -1.236945386 x = -1.236945386 Simplifying x = -1.236945386Subproblem 2
x + 18 = -16.763054614 Simplifying x + 18 = -16.763054614 Reorder the terms: 18 + x = -16.763054614 Solving 18 + x = -16.763054614 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18' to each side of the equation. 18 + -18 + x = -16.763054614 + -18 Combine like terms: 18 + -18 = 0 0 + x = -16.763054614 + -18 x = -16.763054614 + -18 Combine like terms: -16.763054614 + -18 = -34.763054614 x = -34.763054614 Simplifying x = -34.763054614Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.236945386, -34.763054614}
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