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Simplifying 274 = (220 + -1x) * 1.50x + 6x Reorder the terms for easier multiplication: 274 = 1.50x(220 + -1x) + 6x 274 = (220 * 1.50x + -1x * 1.50x) + 6x 274 = (330x + -1.5x2) + 6x Reorder the terms: 274 = 330x + 6x + -1.5x2 Combine like terms: 330x + 6x = 336x 274 = 336x + -1.5x2 Solving 274 = 336x + -1.5x2 Solving for variable 'x'. Reorder the terms: 274 + -336x + 1.5x2 = 336x + -336x + -1.5x2 + 1.5x2 Combine like terms: 336x + -336x = 0 274 + -336x + 1.5x2 = 0 + -1.5x2 + 1.5x2 274 + -336x + 1.5x2 = -1.5x2 + 1.5x2 Combine like terms: -1.5x2 + 1.5x2 = 0.0 274 + -336x + 1.5x2 = 0.0 Begin completing the square. Divide all terms by 1.5 the coefficient of the squared term: Divide each side by '1.5'. 182.6666667 + -224x + x2 = 0 Move the constant term to the right: Add '-182.6666667' to each side of the equation. 182.6666667 + -224x + -182.6666667 + x2 = 0 + -182.6666667 Reorder the terms: 182.6666667 + -182.6666667 + -224x + x2 = 0 + -182.6666667 Combine like terms: 182.6666667 + -182.6666667 = 0.0000000 0.0000000 + -224x + x2 = 0 + -182.6666667 -224x + x2 = 0 + -182.6666667 Combine like terms: 0 + -182.6666667 = -182.6666667 -224x + x2 = -182.6666667 The x term is -224x. Take half its coefficient (-112). Square it (12544) and add it to both sides. Add '12544' to each side of the equation. -224x + 12544 + x2 = -182.6666667 + 12544 Reorder the terms: 12544 + -224x + x2 = -182.6666667 + 12544 Combine like terms: -182.6666667 + 12544 = 12361.3333333 12544 + -224x + x2 = 12361.3333333 Factor a perfect square on the left side: (x + -112)(x + -112) = 12361.3333333 Calculate the square root of the right side: 111.181533239 Break this problem into two subproblems by setting (x + -112) equal to 111.181533239 and -111.181533239.Subproblem 1
x + -112 = 111.181533239 Simplifying x + -112 = 111.181533239 Reorder the terms: -112 + x = 111.181533239 Solving -112 + x = 111.181533239 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '112' to each side of the equation. -112 + 112 + x = 111.181533239 + 112 Combine like terms: -112 + 112 = 0 0 + x = 111.181533239 + 112 x = 111.181533239 + 112 Combine like terms: 111.181533239 + 112 = 223.181533239 x = 223.181533239 Simplifying x = 223.181533239Subproblem 2
x + -112 = -111.181533239 Simplifying x + -112 = -111.181533239 Reorder the terms: -112 + x = -111.181533239 Solving -112 + x = -111.181533239 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '112' to each side of the equation. -112 + 112 + x = -111.181533239 + 112 Combine like terms: -112 + 112 = 0 0 + x = -111.181533239 + 112 x = -111.181533239 + 112 Combine like terms: -111.181533239 + 112 = 0.818466761 x = 0.818466761 Simplifying x = 0.818466761Solution
The solution to the problem is based on the solutions from the subproblems. x = {223.181533239, 0.818466761}
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