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Simplifying x2 + 36x = 36100 Reorder the terms: 36x + x2 = 36100 Solving 36x + x2 = 36100 Solving for variable 'x'. Reorder the terms: -36100 + 36x + x2 = 36100 + -36100 Combine like terms: 36100 + -36100 = 0 -36100 + 36x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '36100' to each side of the equation. -36100 + 36x + 36100 + x2 = 0 + 36100 Reorder the terms: -36100 + 36100 + 36x + x2 = 0 + 36100 Combine like terms: -36100 + 36100 = 0 0 + 36x + x2 = 0 + 36100 36x + x2 = 0 + 36100 Combine like terms: 0 + 36100 = 36100 36x + x2 = 36100 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 = 36100 + 324 Reorder the terms: 324 + 36x + x2 = 36100 + 324 Combine like terms: 36100 + 324 = 36424 324 + 36x + x2 = 36424 Factor a perfect square on the left side: (x + 18)(x + 18) = 36424 Calculate the square root of the right side: 190.850727009 Break this problem into two subproblems by setting (x + 18) equal to 190.850727009 and -190.850727009.Subproblem 1
x + 18 = 190.850727009 Simplifying x + 18 = 190.850727009 Reorder the terms: 18 + x = 190.850727009 Solving 18 + x = 190.850727009 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 = 190.850727009 + -18 Combine like terms: 18 + -18 = 0 0 + x = 190.850727009 + -18 x = 190.850727009 + -18 Combine like terms: 190.850727009 + -18 = 172.850727009 x = 172.850727009 Simplifying x = 172.850727009Subproblem 2
x + 18 = -190.850727009 Simplifying x + 18 = -190.850727009 Reorder the terms: 18 + x = -190.850727009 Solving 18 + x = -190.850727009 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 = -190.850727009 + -18 Combine like terms: 18 + -18 = 0 0 + x = -190.850727009 + -18 x = -190.850727009 + -18 Combine like terms: -190.850727009 + -18 = -208.850727009 x = -208.850727009 Simplifying x = -208.850727009Solution
The solution to the problem is based on the solutions from the subproblems. x = {172.850727009, -208.850727009}
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