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Simplifying (x2 + -6x) + -50(x2 + -6x) + -275 = 0 Reorder the terms: (-6x + x2) + -50(x2 + -6x) + -275 = 0 Remove parenthesis around (-6x + x2) -6x + x2 + -50(x2 + -6x) + -275 = 0 Reorder the terms: -6x + x2 + -50(-6x + x2) + -275 = 0 -6x + x2 + (-6x * -50 + x2 * -50) + -275 = 0 -6x + x2 + (300x + -50x2) + -275 = 0 Reorder the terms: -275 + -6x + 300x + x2 + -50x2 = 0 Combine like terms: -6x + 300x = 294x -275 + 294x + x2 + -50x2 = 0 Combine like terms: x2 + -50x2 = -49x2 -275 + 294x + -49x2 = 0 Solving -275 + 294x + -49x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -49 the coefficient of the squared term: Divide each side by '-49'. 5.612244898 + -6x + x2 = 0 Move the constant term to the right: Add '-5.612244898' to each side of the equation. 5.612244898 + -6x + -5.612244898 + x2 = 0 + -5.612244898 Reorder the terms: 5.612244898 + -5.612244898 + -6x + x2 = 0 + -5.612244898 Combine like terms: 5.612244898 + -5.612244898 = 0.000000000 0.000000000 + -6x + x2 = 0 + -5.612244898 -6x + x2 = 0 + -5.612244898 Combine like terms: 0 + -5.612244898 = -5.612244898 -6x + x2 = -5.612244898 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = -5.612244898 + 9 Reorder the terms: 9 + -6x + x2 = -5.612244898 + 9 Combine like terms: -5.612244898 + 9 = 3.387755102 9 + -6x + x2 = 3.387755102 Factor a perfect square on the left side: (x + -3)(x + -3) = 3.387755102 Calculate the square root of the right side: 1.840585532 Break this problem into two subproblems by setting (x + -3) equal to 1.840585532 and -1.840585532.Subproblem 1
x + -3 = 1.840585532 Simplifying x + -3 = 1.840585532 Reorder the terms: -3 + x = 1.840585532 Solving -3 + x = 1.840585532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 1.840585532 + 3 Combine like terms: -3 + 3 = 0 0 + x = 1.840585532 + 3 x = 1.840585532 + 3 Combine like terms: 1.840585532 + 3 = 4.840585532 x = 4.840585532 Simplifying x = 4.840585532Subproblem 2
x + -3 = -1.840585532 Simplifying x + -3 = -1.840585532 Reorder the terms: -3 + x = -1.840585532 Solving -3 + x = -1.840585532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -1.840585532 + 3 Combine like terms: -3 + 3 = 0 0 + x = -1.840585532 + 3 x = -1.840585532 + 3 Combine like terms: -1.840585532 + 3 = 1.159414468 x = 1.159414468 Simplifying x = 1.159414468Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.840585532, 1.159414468}
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