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Simplifying x2 + 36x + 36 = -5 Reorder the terms: 36 + 36x + x2 = -5 Solving 36 + 36x + x2 = -5 Solving for variable 'x'. Reorder the terms: 36 + 5 + 36x + x2 = -5 + 5 Combine like terms: 36 + 5 = 41 41 + 36x + x2 = -5 + 5 Combine like terms: -5 + 5 = 0 41 + 36x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-41' to each side of the equation. 41 + 36x + -41 + x2 = 0 + -41 Reorder the terms: 41 + -41 + 36x + x2 = 0 + -41 Combine like terms: 41 + -41 = 0 0 + 36x + x2 = 0 + -41 36x + x2 = 0 + -41 Combine like terms: 0 + -41 = -41 36x + x2 = -41 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 = -41 + 324 Reorder the terms: 324 + 36x + x2 = -41 + 324 Combine like terms: -41 + 324 = 283 324 + 36x + x2 = 283 Factor a perfect square on the left side: (x + 18)(x + 18) = 283 Calculate the square root of the right side: 16.822603841 Break this problem into two subproblems by setting (x + 18) equal to 16.822603841 and -16.822603841.Subproblem 1
x + 18 = 16.822603841 Simplifying x + 18 = 16.822603841 Reorder the terms: 18 + x = 16.822603841 Solving 18 + x = 16.822603841 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 = 16.822603841 + -18 Combine like terms: 18 + -18 = 0 0 + x = 16.822603841 + -18 x = 16.822603841 + -18 Combine like terms: 16.822603841 + -18 = -1.177396159 x = -1.177396159 Simplifying x = -1.177396159Subproblem 2
x + 18 = -16.822603841 Simplifying x + 18 = -16.822603841 Reorder the terms: 18 + x = -16.822603841 Solving 18 + x = -16.822603841 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 = -16.822603841 + -18 Combine like terms: 18 + -18 = 0 0 + x = -16.822603841 + -18 x = -16.822603841 + -18 Combine like terms: -16.822603841 + -18 = -34.822603841 x = -34.822603841 Simplifying x = -34.822603841Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.177396159, -34.822603841}
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