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Simplifying 226.24x = 2222.22 + 5.56x2 Solving 226.24x = 2222.22 + 5.56x2 Solving for variable 'x'. Reorder the terms: -2222.22 + 226.24x + -5.56x2 = 2222.22 + 5.56x2 + -2222.22 + -5.56x2 Reorder the terms: -2222.22 + 226.24x + -5.56x2 = 2222.22 + -2222.22 + 5.56x2 + -5.56x2 Combine like terms: 2222.22 + -2222.22 = 0.00 -2222.22 + 226.24x + -5.56x2 = 0.00 + 5.56x2 + -5.56x2 -2222.22 + 226.24x + -5.56x2 = 5.56x2 + -5.56x2 Combine like terms: 5.56x2 + -5.56x2 = 0.00 -2222.22 + 226.24x + -5.56x2 = 0.00 Begin completing the square. Divide all terms by -5.56 the coefficient of the squared term: Divide each side by '-5.56'. 399.6798561 + -40.69064748x + x2 = 0 Move the constant term to the right: Add '-399.6798561' to each side of the equation. 399.6798561 + -40.69064748x + -399.6798561 + x2 = 0 + -399.6798561 Reorder the terms: 399.6798561 + -399.6798561 + -40.69064748x + x2 = 0 + -399.6798561 Combine like terms: 399.6798561 + -399.6798561 = 0.0000000 0.0000000 + -40.69064748x + x2 = 0 + -399.6798561 -40.69064748x + x2 = 0 + -399.6798561 Combine like terms: 0 + -399.6798561 = -399.6798561 -40.69064748x + x2 = -399.6798561 The x term is -40.69064748x. Take half its coefficient (-20.34532374). Square it (413.9321981) and add it to both sides. Add '413.9321981' to each side of the equation. -40.69064748x + 413.9321981 + x2 = -399.6798561 + 413.9321981 Reorder the terms: 413.9321981 + -40.69064748x + x2 = -399.6798561 + 413.9321981 Combine like terms: -399.6798561 + 413.9321981 = 14.252342 413.9321981 + -40.69064748x + x2 = 14.252342 Factor a perfect square on the left side: (x + -20.34532374)(x + -20.34532374) = 14.252342 Calculate the square root of the right side: 3.77522741 Break this problem into two subproblems by setting (x + -20.34532374) equal to 3.77522741 and -3.77522741.Subproblem 1
x + -20.34532374 = 3.77522741 Simplifying x + -20.34532374 = 3.77522741 Reorder the terms: -20.34532374 + x = 3.77522741 Solving -20.34532374 + x = 3.77522741 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20.34532374' to each side of the equation. -20.34532374 + 20.34532374 + x = 3.77522741 + 20.34532374 Combine like terms: -20.34532374 + 20.34532374 = 0.00000000 0.00000000 + x = 3.77522741 + 20.34532374 x = 3.77522741 + 20.34532374 Combine like terms: 3.77522741 + 20.34532374 = 24.12055115 x = 24.12055115 Simplifying x = 24.12055115Subproblem 2
x + -20.34532374 = -3.77522741 Simplifying x + -20.34532374 = -3.77522741 Reorder the terms: -20.34532374 + x = -3.77522741 Solving -20.34532374 + x = -3.77522741 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20.34532374' to each side of the equation. -20.34532374 + 20.34532374 + x = -3.77522741 + 20.34532374 Combine like terms: -20.34532374 + 20.34532374 = 0.00000000 0.00000000 + x = -3.77522741 + 20.34532374 x = -3.77522741 + 20.34532374 Combine like terms: -3.77522741 + 20.34532374 = 16.57009633 x = 16.57009633 Simplifying x = 16.57009633Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.12055115, 16.57009633}
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