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Simplifying x2 + 36x + -324 = 0 Reorder the terms: -324 + 36x + x2 = 0 Solving -324 + 36x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '324' to each side of the equation. -324 + 36x + 324 + x2 = 0 + 324 Reorder the terms: -324 + 324 + 36x + x2 = 0 + 324 Combine like terms: -324 + 324 = 0 0 + 36x + x2 = 0 + 324 36x + x2 = 0 + 324 Combine like terms: 0 + 324 = 324 36x + x2 = 324 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 = 324 + 324 Reorder the terms: 324 + 36x + x2 = 324 + 324 Combine like terms: 324 + 324 = 648 324 + 36x + x2 = 648 Factor a perfect square on the left side: (x + 18)(x + 18) = 648 Calculate the square root of the right side: 25.455844123 Break this problem into two subproblems by setting (x + 18) equal to 25.455844123 and -25.455844123.Subproblem 1
x + 18 = 25.455844123 Simplifying x + 18 = 25.455844123 Reorder the terms: 18 + x = 25.455844123 Solving 18 + x = 25.455844123 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 = 25.455844123 + -18 Combine like terms: 18 + -18 = 0 0 + x = 25.455844123 + -18 x = 25.455844123 + -18 Combine like terms: 25.455844123 + -18 = 7.455844123 x = 7.455844123 Simplifying x = 7.455844123Subproblem 2
x + 18 = -25.455844123 Simplifying x + 18 = -25.455844123 Reorder the terms: 18 + x = -25.455844123 Solving 18 + x = -25.455844123 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 = -25.455844123 + -18 Combine like terms: 18 + -18 = 0 0 + x = -25.455844123 + -18 x = -25.455844123 + -18 Combine like terms: -25.455844123 + -18 = -43.455844123 x = -43.455844123 Simplifying x = -43.455844123Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.455844123, -43.455844123}
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