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Simplifying 0 = 11x2 + -324x + -2200 Reorder the terms: 0 = -2200 + -324x + 11x2 Solving 0 = -2200 + -324x + 11x2 Solving for variable 'x'. Combine like terms: 0 + 2200 = 2200 2200 + 324x + -11x2 = -2200 + -324x + 11x2 + 2200 + 324x + -11x2 Reorder the terms: 2200 + 324x + -11x2 = -2200 + 2200 + -324x + 324x + 11x2 + -11x2 Combine like terms: -2200 + 2200 = 0 2200 + 324x + -11x2 = 0 + -324x + 324x + 11x2 + -11x2 2200 + 324x + -11x2 = -324x + 324x + 11x2 + -11x2 Combine like terms: -324x + 324x = 0 2200 + 324x + -11x2 = 0 + 11x2 + -11x2 2200 + 324x + -11x2 = 11x2 + -11x2 Combine like terms: 11x2 + -11x2 = 0 2200 + 324x + -11x2 = 0 Begin completing the square. Divide all terms by -11 the coefficient of the squared term: Divide each side by '-11'. -200 + -29.45454545x + x2 = 0 Move the constant term to the right: Add '200' to each side of the equation. -200 + -29.45454545x + 200 + x2 = 0 + 200 Reorder the terms: -200 + 200 + -29.45454545x + x2 = 0 + 200 Combine like terms: -200 + 200 = 0 0 + -29.45454545x + x2 = 0 + 200 -29.45454545x + x2 = 0 + 200 Combine like terms: 0 + 200 = 200 -29.45454545x + x2 = 200 The x term is -29.45454545x. Take half its coefficient (-14.72727273). Square it (216.8925621) and add it to both sides. Add '216.8925621' to each side of the equation. -29.45454545x + 216.8925621 + x2 = 200 + 216.8925621 Reorder the terms: 216.8925621 + -29.45454545x + x2 = 200 + 216.8925621 Combine like terms: 200 + 216.8925621 = 416.8925621 216.8925621 + -29.45454545x + x2 = 416.8925621 Factor a perfect square on the left side: (x + -14.72727273)(x + -14.72727273) = 416.8925621 Calculate the square root of the right side: 20.417947059 Break this problem into two subproblems by setting (x + -14.72727273) equal to 20.417947059 and -20.417947059.Subproblem 1
x + -14.72727273 = 20.417947059 Simplifying x + -14.72727273 = 20.417947059 Reorder the terms: -14.72727273 + x = 20.417947059 Solving -14.72727273 + x = 20.417947059 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14.72727273' to each side of the equation. -14.72727273 + 14.72727273 + x = 20.417947059 + 14.72727273 Combine like terms: -14.72727273 + 14.72727273 = 0.00000000 0.00000000 + x = 20.417947059 + 14.72727273 x = 20.417947059 + 14.72727273 Combine like terms: 20.417947059 + 14.72727273 = 35.145219789 x = 35.145219789 Simplifying x = 35.145219789Subproblem 2
x + -14.72727273 = -20.417947059 Simplifying x + -14.72727273 = -20.417947059 Reorder the terms: -14.72727273 + x = -20.417947059 Solving -14.72727273 + x = -20.417947059 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14.72727273' to each side of the equation. -14.72727273 + 14.72727273 + x = -20.417947059 + 14.72727273 Combine like terms: -14.72727273 + 14.72727273 = 0.00000000 0.00000000 + x = -20.417947059 + 14.72727273 x = -20.417947059 + 14.72727273 Combine like terms: -20.417947059 + 14.72727273 = -5.690674329 x = -5.690674329 Simplifying x = -5.690674329Solution
The solution to the problem is based on the solutions from the subproblems. x = {35.145219789, -5.690674329}
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