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Simplifying x2 + 36x + -25 = 0 Reorder the terms: -25 + 36x + x2 = 0 Solving -25 + 36x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '25' to each side of the equation. -25 + 36x + 25 + x2 = 0 + 25 Reorder the terms: -25 + 25 + 36x + x2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + 36x + x2 = 0 + 25 36x + x2 = 0 + 25 Combine like terms: 0 + 25 = 25 36x + x2 = 25 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 = 25 + 324 Reorder the terms: 324 + 36x + x2 = 25 + 324 Combine like terms: 25 + 324 = 349 324 + 36x + x2 = 349 Factor a perfect square on the left side: (x + 18)(x + 18) = 349 Calculate the square root of the right side: 18.681541692 Break this problem into two subproblems by setting (x + 18) equal to 18.681541692 and -18.681541692.Subproblem 1
x + 18 = 18.681541692 Simplifying x + 18 = 18.681541692 Reorder the terms: 18 + x = 18.681541692 Solving 18 + x = 18.681541692 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 = 18.681541692 + -18 Combine like terms: 18 + -18 = 0 0 + x = 18.681541692 + -18 x = 18.681541692 + -18 Combine like terms: 18.681541692 + -18 = 0.681541692 x = 0.681541692 Simplifying x = 0.681541692Subproblem 2
x + 18 = -18.681541692 Simplifying x + 18 = -18.681541692 Reorder the terms: 18 + x = -18.681541692 Solving 18 + x = -18.681541692 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 = -18.681541692 + -18 Combine like terms: 18 + -18 = 0 0 + x = -18.681541692 + -18 x = -18.681541692 + -18 Combine like terms: -18.681541692 + -18 = -36.681541692 x = -36.681541692 Simplifying x = -36.681541692Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.681541692, -36.681541692}
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