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Simplifying x2 + 36x + -39 = 0 Reorder the terms: -39 + 36x + x2 = 0 Solving -39 + 36x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '39' to each side of the equation. -39 + 36x + 39 + x2 = 0 + 39 Reorder the terms: -39 + 39 + 36x + x2 = 0 + 39 Combine like terms: -39 + 39 = 0 0 + 36x + x2 = 0 + 39 36x + x2 = 0 + 39 Combine like terms: 0 + 39 = 39 36x + x2 = 39 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 = 39 + 324 Reorder the terms: 324 + 36x + x2 = 39 + 324 Combine like terms: 39 + 324 = 363 324 + 36x + x2 = 363 Factor a perfect square on the left side: (x + 18)(x + 18) = 363 Calculate the square root of the right side: 19.052558883 Break this problem into two subproblems by setting (x + 18) equal to 19.052558883 and -19.052558883.Subproblem 1
x + 18 = 19.052558883 Simplifying x + 18 = 19.052558883 Reorder the terms: 18 + x = 19.052558883 Solving 18 + x = 19.052558883 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 = 19.052558883 + -18 Combine like terms: 18 + -18 = 0 0 + x = 19.052558883 + -18 x = 19.052558883 + -18 Combine like terms: 19.052558883 + -18 = 1.052558883 x = 1.052558883 Simplifying x = 1.052558883Subproblem 2
x + 18 = -19.052558883 Simplifying x + 18 = -19.052558883 Reorder the terms: 18 + x = -19.052558883 Solving 18 + x = -19.052558883 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 = -19.052558883 + -18 Combine like terms: 18 + -18 = 0 0 + x = -19.052558883 + -18 x = -19.052558883 + -18 Combine like terms: -19.052558883 + -18 = -37.052558883 x = -37.052558883 Simplifying x = -37.052558883Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.052558883, -37.052558883}
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