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Simplifying 120 = 0.05x2 + 22x Reorder the terms: 120 = 22x + 0.05x2 Solving 120 = 22x + 0.05x2 Solving for variable 'x'. Reorder the terms: 120 + -22x + -0.05x2 = 22x + -22x + 0.05x2 + -0.05x2 Combine like terms: 22x + -22x = 0 120 + -22x + -0.05x2 = 0 + 0.05x2 + -0.05x2 120 + -22x + -0.05x2 = 0.05x2 + -0.05x2 Combine like terms: 0.05x2 + -0.05x2 = 0.00 120 + -22x + -0.05x2 = 0.00 Begin completing the square. Divide all terms by -0.05 the coefficient of the squared term: Divide each side by '-0.05'. -2400 + 440x + x2 = 0 Move the constant term to the right: Add '2400' to each side of the equation. -2400 + 440x + 2400 + x2 = 0 + 2400 Reorder the terms: -2400 + 2400 + 440x + x2 = 0 + 2400 Combine like terms: -2400 + 2400 = 0 0 + 440x + x2 = 0 + 2400 440x + x2 = 0 + 2400 Combine like terms: 0 + 2400 = 2400 440x + x2 = 2400 The x term is 440x. Take half its coefficient (220). Square it (48400) and add it to both sides. Add '48400' to each side of the equation. 440x + 48400 + x2 = 2400 + 48400 Reorder the terms: 48400 + 440x + x2 = 2400 + 48400 Combine like terms: 2400 + 48400 = 50800 48400 + 440x + x2 = 50800 Factor a perfect square on the left side: (x + 220)(x + 220) = 50800 Calculate the square root of the right side: 225.388553392 Break this problem into two subproblems by setting (x + 220) equal to 225.388553392 and -225.388553392.Subproblem 1
x + 220 = 225.388553392 Simplifying x + 220 = 225.388553392 Reorder the terms: 220 + x = 225.388553392 Solving 220 + x = 225.388553392 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-220' to each side of the equation. 220 + -220 + x = 225.388553392 + -220 Combine like terms: 220 + -220 = 0 0 + x = 225.388553392 + -220 x = 225.388553392 + -220 Combine like terms: 225.388553392 + -220 = 5.388553392 x = 5.388553392 Simplifying x = 5.388553392Subproblem 2
x + 220 = -225.388553392 Simplifying x + 220 = -225.388553392 Reorder the terms: 220 + x = -225.388553392 Solving 220 + x = -225.388553392 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-220' to each side of the equation. 220 + -220 + x = -225.388553392 + -220 Combine like terms: 220 + -220 = 0 0 + x = -225.388553392 + -220 x = -225.388553392 + -220 Combine like terms: -225.388553392 + -220 = -445.388553392 x = -445.388553392 Simplifying x = -445.388553392Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.388553392, -445.388553392}
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