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Simplifying 20(500 + -2.2x) = x * x (500 * 20 + -2.2x * 20) = x * x (10000 + -44x) = x * x Multiply x * x 10000 + -44x = x2 Solving 10000 + -44x = x2 Solving for variable 'x'. Combine like terms: x2 + -1x2 = 0 10000 + -44x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -10000 + 44x + x2 = 0 Move the constant term to the right: Add '10000' to each side of the equation. -10000 + 44x + 10000 + x2 = 0 + 10000 Reorder the terms: -10000 + 10000 + 44x + x2 = 0 + 10000 Combine like terms: -10000 + 10000 = 0 0 + 44x + x2 = 0 + 10000 44x + x2 = 0 + 10000 Combine like terms: 0 + 10000 = 10000 44x + x2 = 10000 The x term is 44x. Take half its coefficient (22). Square it (484) and add it to both sides. Add '484' to each side of the equation. 44x + 484 + x2 = 10000 + 484 Reorder the terms: 484 + 44x + x2 = 10000 + 484 Combine like terms: 10000 + 484 = 10484 484 + 44x + x2 = 10484 Factor a perfect square on the left side: (x + 22)(x + 22) = 10484 Calculate the square root of the right side: 102.391405889 Break this problem into two subproblems by setting (x + 22) equal to 102.391405889 and -102.391405889.Subproblem 1
x + 22 = 102.391405889 Simplifying x + 22 = 102.391405889 Reorder the terms: 22 + x = 102.391405889 Solving 22 + x = 102.391405889 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-22' to each side of the equation. 22 + -22 + x = 102.391405889 + -22 Combine like terms: 22 + -22 = 0 0 + x = 102.391405889 + -22 x = 102.391405889 + -22 Combine like terms: 102.391405889 + -22 = 80.391405889 x = 80.391405889 Simplifying x = 80.391405889Subproblem 2
x + 22 = -102.391405889 Simplifying x + 22 = -102.391405889 Reorder the terms: 22 + x = -102.391405889 Solving 22 + x = -102.391405889 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-22' to each side of the equation. 22 + -22 + x = -102.391405889 + -22 Combine like terms: 22 + -22 = 0 0 + x = -102.391405889 + -22 x = -102.391405889 + -22 Combine like terms: -102.391405889 + -22 = -124.391405889 x = -124.391405889 Simplifying x = -124.391405889Solution
The solution to the problem is based on the solutions from the subproblems. x = {80.391405889, -124.391405889}
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