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Simplifying x2 + 36x + 87 = 0 Reorder the terms: 87 + 36x + x2 = 0 Solving 87 + 36x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-87' to each side of the equation. 87 + 36x + -87 + x2 = 0 + -87 Reorder the terms: 87 + -87 + 36x + x2 = 0 + -87 Combine like terms: 87 + -87 = 0 0 + 36x + x2 = 0 + -87 36x + x2 = 0 + -87 Combine like terms: 0 + -87 = -87 36x + x2 = -87 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 = -87 + 324 Reorder the terms: 324 + 36x + x2 = -87 + 324 Combine like terms: -87 + 324 = 237 324 + 36x + x2 = 237 Factor a perfect square on the left side: (x + 18)(x + 18) = 237 Calculate the square root of the right side: 15.394804318 Break this problem into two subproblems by setting (x + 18) equal to 15.394804318 and -15.394804318.Subproblem 1
x + 18 = 15.394804318 Simplifying x + 18 = 15.394804318 Reorder the terms: 18 + x = 15.394804318 Solving 18 + x = 15.394804318 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 = 15.394804318 + -18 Combine like terms: 18 + -18 = 0 0 + x = 15.394804318 + -18 x = 15.394804318 + -18 Combine like terms: 15.394804318 + -18 = -2.605195682 x = -2.605195682 Simplifying x = -2.605195682Subproblem 2
x + 18 = -15.394804318 Simplifying x + 18 = -15.394804318 Reorder the terms: 18 + x = -15.394804318 Solving 18 + x = -15.394804318 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 = -15.394804318 + -18 Combine like terms: 18 + -18 = 0 0 + x = -15.394804318 + -18 x = -15.394804318 + -18 Combine like terms: -15.394804318 + -18 = -33.394804318 x = -33.394804318 Simplifying x = -33.394804318Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.605195682, -33.394804318}
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