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Simplifying (0.25x2) + -9x + -7000 = 0 Reorder the terms: -7000 + -9x + (0.25x2) = 0 Solving -7000 + -9x + (0.25x2) = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.25 the coefficient of the squared term: Divide each side by '0.25'. -28000 + -36x + x2 = 0 Move the constant term to the right: Add '28000' to each side of the equation. -28000 + -36x + 28000 + x2 = 0 + 28000 Reorder the terms: -28000 + 28000 + -36x + x2 = 0 + 28000 Combine like terms: -28000 + 28000 = 0 0 + -36x + x2 = 0 + 28000 -36x + x2 = 0 + 28000 Combine like terms: 0 + 28000 = 28000 -36x + x2 = 28000 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 = 28000 + 324 Reorder the terms: 324 + -36x + x2 = 28000 + 324 Combine like terms: 28000 + 324 = 28324 324 + -36x + x2 = 28324 Factor a perfect square on the left side: ((x) + -18)((x) + -18) = 28324 Calculate the square root of the right side: 168.297355891 Break this problem into two subproblems by setting ((x) + -18) equal to 168.297355891 and -168.297355891.Subproblem 1
(x) + -18 = 168.297355891 Simplifying (x) + -18 = 168.297355891 x + -18 = 168.297355891 Reorder the terms: -18 + x = 168.297355891 Solving -18 + x = 168.297355891 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 = 168.297355891 + 18 Combine like terms: -18 + 18 = 0 0 + x = 168.297355891 + 18 x = 168.297355891 + 18 Combine like terms: 168.297355891 + 18 = 186.297355891 x = 186.297355891 Simplifying x = 186.297355891Subproblem 2
(x) + -18 = -168.297355891 Simplifying (x) + -18 = -168.297355891 x + -18 = -168.297355891 Reorder the terms: -18 + x = -168.297355891 Solving -18 + x = -168.297355891 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 = -168.297355891 + 18 Combine like terms: -18 + 18 = 0 0 + x = -168.297355891 + 18 x = -168.297355891 + 18 Combine like terms: -168.297355891 + 18 = -150.297355891 x = -150.297355891 Simplifying x = -150.297355891Solution
The solution to the problem is based on the solutions from the subproblems. x = {186.297355891, -150.297355891}
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