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Simplifying x2 + 36x = -42 Reorder the terms: 36x + x2 = -42 Solving 36x + x2 = -42 Solving for variable 'x'. Reorder the terms: 42 + 36x + x2 = -42 + 42 Combine like terms: -42 + 42 = 0 42 + 36x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-42' to each side of the equation. 42 + 36x + -42 + x2 = 0 + -42 Reorder the terms: 42 + -42 + 36x + x2 = 0 + -42 Combine like terms: 42 + -42 = 0 0 + 36x + x2 = 0 + -42 36x + x2 = 0 + -42 Combine like terms: 0 + -42 = -42 36x + x2 = -42 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 = -42 + 324 Reorder the terms: 324 + 36x + x2 = -42 + 324 Combine like terms: -42 + 324 = 282 324 + 36x + x2 = 282 Factor a perfect square on the left side: (x + 18)(x + 18) = 282 Calculate the square root of the right side: 16.792855624 Break this problem into two subproblems by setting (x + 18) equal to 16.792855624 and -16.792855624.Subproblem 1
x + 18 = 16.792855624 Simplifying x + 18 = 16.792855624 Reorder the terms: 18 + x = 16.792855624 Solving 18 + x = 16.792855624 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 = 16.792855624 + -18 Combine like terms: 18 + -18 = 0 0 + x = 16.792855624 + -18 x = 16.792855624 + -18 Combine like terms: 16.792855624 + -18 = -1.207144376 x = -1.207144376 Simplifying x = -1.207144376Subproblem 2
x + 18 = -16.792855624 Simplifying x + 18 = -16.792855624 Reorder the terms: 18 + x = -16.792855624 Solving 18 + x = -16.792855624 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 = -16.792855624 + -18 Combine like terms: 18 + -18 = 0 0 + x = -16.792855624 + -18 x = -16.792855624 + -18 Combine like terms: -16.792855624 + -18 = -34.792855624 x = -34.792855624 Simplifying x = -34.792855624Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.207144376, -34.792855624}
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