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Simplifying 0 = -2.2x2 + 550x + -2260 Reorder the terms: 0 = -2260 + 550x + -2.2x2 Solving 0 = -2260 + 550x + -2.2x2 Solving for variable 'x'. Combine like terms: 0 + 2260 = 2260 2260 + -550x + 2.2x2 = -2260 + 550x + -2.2x2 + 2260 + -550x + 2.2x2 Reorder the terms: 2260 + -550x + 2.2x2 = -2260 + 2260 + 550x + -550x + -2.2x2 + 2.2x2 Combine like terms: -2260 + 2260 = 0 2260 + -550x + 2.2x2 = 0 + 550x + -550x + -2.2x2 + 2.2x2 2260 + -550x + 2.2x2 = 550x + -550x + -2.2x2 + 2.2x2 Combine like terms: 550x + -550x = 0 2260 + -550x + 2.2x2 = 0 + -2.2x2 + 2.2x2 2260 + -550x + 2.2x2 = -2.2x2 + 2.2x2 Combine like terms: -2.2x2 + 2.2x2 = 0.0 2260 + -550x + 2.2x2 = 0.0 Begin completing the square. Divide all terms by 2.2 the coefficient of the squared term: Divide each side by '2.2'. 1027.272727 + -250x + x2 = 0 Move the constant term to the right: Add '-1027.272727' to each side of the equation. 1027.272727 + -250x + -1027.272727 + x2 = 0 + -1027.272727 Reorder the terms: 1027.272727 + -1027.272727 + -250x + x2 = 0 + -1027.272727 Combine like terms: 1027.272727 + -1027.272727 = 0.000000 0.000000 + -250x + x2 = 0 + -1027.272727 -250x + x2 = 0 + -1027.272727 Combine like terms: 0 + -1027.272727 = -1027.272727 -250x + x2 = -1027.272727 The x term is -250x. Take half its coefficient (-125). Square it (15625) and add it to both sides. Add '15625' to each side of the equation. -250x + 15625 + x2 = -1027.272727 + 15625 Reorder the terms: 15625 + -250x + x2 = -1027.272727 + 15625 Combine like terms: -1027.272727 + 15625 = 14597.727273 15625 + -250x + x2 = 14597.727273 Factor a perfect square on the left side: (x + -125)(x + -125) = 14597.727273 Calculate the square root of the right side: 120.821054759 Break this problem into two subproblems by setting (x + -125) equal to 120.821054759 and -120.821054759.Subproblem 1
x + -125 = 120.821054759 Simplifying x + -125 = 120.821054759 Reorder the terms: -125 + x = 120.821054759 Solving -125 + x = 120.821054759 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '125' to each side of the equation. -125 + 125 + x = 120.821054759 + 125 Combine like terms: -125 + 125 = 0 0 + x = 120.821054759 + 125 x = 120.821054759 + 125 Combine like terms: 120.821054759 + 125 = 245.821054759 x = 245.821054759 Simplifying x = 245.821054759Subproblem 2
x + -125 = -120.821054759 Simplifying x + -125 = -120.821054759 Reorder the terms: -125 + x = -120.821054759 Solving -125 + x = -120.821054759 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '125' to each side of the equation. -125 + 125 + x = -120.821054759 + 125 Combine like terms: -125 + 125 = 0 0 + x = -120.821054759 + 125 x = -120.821054759 + 125 Combine like terms: -120.821054759 + 125 = 4.178945241 x = 4.178945241 Simplifying x = 4.178945241Solution
The solution to the problem is based on the solutions from the subproblems. x = {245.821054759, 4.178945241}
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