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Simplifying 200x + -1x2 = -20x + 450 Reorder the terms: 200x + -1x2 = 450 + -20x Solving 200x + -1x2 = 450 + -20x Solving for variable 'x'. Reorder the terms: -450 + 200x + 20x + -1x2 = 450 + -20x + -450 + 20x Combine like terms: 200x + 20x = 220x -450 + 220x + -1x2 = 450 + -20x + -450 + 20x Reorder the terms: -450 + 220x + -1x2 = 450 + -450 + -20x + 20x Combine like terms: 450 + -450 = 0 -450 + 220x + -1x2 = 0 + -20x + 20x -450 + 220x + -1x2 = -20x + 20x Combine like terms: -20x + 20x = 0 -450 + 220x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 450 + -220x + x2 = 0 Move the constant term to the right: Add '-450' to each side of the equation. 450 + -220x + -450 + x2 = 0 + -450 Reorder the terms: 450 + -450 + -220x + x2 = 0 + -450 Combine like terms: 450 + -450 = 0 0 + -220x + x2 = 0 + -450 -220x + x2 = 0 + -450 Combine like terms: 0 + -450 = -450 -220x + x2 = -450 The x term is -220x. Take half its coefficient (-110). Square it (12100) and add it to both sides. Add '12100' to each side of the equation. -220x + 12100 + x2 = -450 + 12100 Reorder the terms: 12100 + -220x + x2 = -450 + 12100 Combine like terms: -450 + 12100 = 11650 12100 + -220x + x2 = 11650 Factor a perfect square on the left side: (x + -110)(x + -110) = 11650 Calculate the square root of the right side: 107.935165725 Break this problem into two subproblems by setting (x + -110) equal to 107.935165725 and -107.935165725.Subproblem 1
x + -110 = 107.935165725 Simplifying x + -110 = 107.935165725 Reorder the terms: -110 + x = 107.935165725 Solving -110 + x = 107.935165725 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '110' to each side of the equation. -110 + 110 + x = 107.935165725 + 110 Combine like terms: -110 + 110 = 0 0 + x = 107.935165725 + 110 x = 107.935165725 + 110 Combine like terms: 107.935165725 + 110 = 217.935165725 x = 217.935165725 Simplifying x = 217.935165725Subproblem 2
x + -110 = -107.935165725 Simplifying x + -110 = -107.935165725 Reorder the terms: -110 + x = -107.935165725 Solving -110 + x = -107.935165725 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '110' to each side of the equation. -110 + 110 + x = -107.935165725 + 110 Combine like terms: -110 + 110 = 0 0 + x = -107.935165725 + 110 x = -107.935165725 + 110 Combine like terms: -107.935165725 + 110 = 2.064834275 x = 2.064834275 Simplifying x = 2.064834275Solution
The solution to the problem is based on the solutions from the subproblems. x = {217.935165725, 2.064834275}
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