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Simplifying x2 + -36x + 168 = 0 Reorder the terms: 168 + -36x + x2 = 0 Solving 168 + -36x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-168' to each side of the equation. 168 + -36x + -168 + x2 = 0 + -168 Reorder the terms: 168 + -168 + -36x + x2 = 0 + -168 Combine like terms: 168 + -168 = 0 0 + -36x + x2 = 0 + -168 -36x + x2 = 0 + -168 Combine like terms: 0 + -168 = -168 -36x + x2 = -168 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 = -168 + 324 Reorder the terms: 324 + -36x + x2 = -168 + 324 Combine like terms: -168 + 324 = 156 324 + -36x + x2 = 156 Factor a perfect square on the left side: (x + -18)(x + -18) = 156 Calculate the square root of the right side: 12.489995997 Break this problem into two subproblems by setting (x + -18) equal to 12.489995997 and -12.489995997.Subproblem 1
x + -18 = 12.489995997 Simplifying x + -18 = 12.489995997 Reorder the terms: -18 + x = 12.489995997 Solving -18 + x = 12.489995997 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 = 12.489995997 + 18 Combine like terms: -18 + 18 = 0 0 + x = 12.489995997 + 18 x = 12.489995997 + 18 Combine like terms: 12.489995997 + 18 = 30.489995997 x = 30.489995997 Simplifying x = 30.489995997Subproblem 2
x + -18 = -12.489995997 Simplifying x + -18 = -12.489995997 Reorder the terms: -18 + x = -12.489995997 Solving -18 + x = -12.489995997 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 = -12.489995997 + 18 Combine like terms: -18 + 18 = 0 0 + x = -12.489995997 + 18 x = -12.489995997 + 18 Combine like terms: -12.489995997 + 18 = 5.510004003 x = 5.510004003 Simplifying x = 5.510004003Solution
The solution to the problem is based on the solutions from the subproblems. x = {30.489995997, 5.510004003}
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