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Simplifying 244x = x2 + -6x + 28 Reorder the terms: 244x = 28 + -6x + x2 Solving 244x = 28 + -6x + x2 Solving for variable 'x'. Reorder the terms: -28 + 244x + 6x + -1x2 = 28 + -6x + x2 + -28 + 6x + -1x2 Combine like terms: 244x + 6x = 250x -28 + 250x + -1x2 = 28 + -6x + x2 + -28 + 6x + -1x2 Reorder the terms: -28 + 250x + -1x2 = 28 + -28 + -6x + 6x + x2 + -1x2 Combine like terms: 28 + -28 = 0 -28 + 250x + -1x2 = 0 + -6x + 6x + x2 + -1x2 -28 + 250x + -1x2 = -6x + 6x + x2 + -1x2 Combine like terms: -6x + 6x = 0 -28 + 250x + -1x2 = 0 + x2 + -1x2 -28 + 250x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -28 + 250x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 28 + -250x + x2 = 0 Move the constant term to the right: Add '-28' to each side of the equation. 28 + -250x + -28 + x2 = 0 + -28 Reorder the terms: 28 + -28 + -250x + x2 = 0 + -28 Combine like terms: 28 + -28 = 0 0 + -250x + x2 = 0 + -28 -250x + x2 = 0 + -28 Combine like terms: 0 + -28 = -28 -250x + x2 = -28 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 = -28 + 15625 Reorder the terms: 15625 + -250x + x2 = -28 + 15625 Combine like terms: -28 + 15625 = 15597 15625 + -250x + x2 = 15597 Factor a perfect square on the left side: (x + -125)(x + -125) = 15597 Calculate the square root of the right side: 124.887949779 Break this problem into two subproblems by setting (x + -125) equal to 124.887949779 and -124.887949779.Subproblem 1
x + -125 = 124.887949779 Simplifying x + -125 = 124.887949779 Reorder the terms: -125 + x = 124.887949779 Solving -125 + x = 124.887949779 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 = 124.887949779 + 125 Combine like terms: -125 + 125 = 0 0 + x = 124.887949779 + 125 x = 124.887949779 + 125 Combine like terms: 124.887949779 + 125 = 249.887949779 x = 249.887949779 Simplifying x = 249.887949779Subproblem 2
x + -125 = -124.887949779 Simplifying x + -125 = -124.887949779 Reorder the terms: -125 + x = -124.887949779 Solving -125 + x = -124.887949779 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 = -124.887949779 + 125 Combine like terms: -125 + 125 = 0 0 + x = -124.887949779 + 125 x = -124.887949779 + 125 Combine like terms: -124.887949779 + 125 = 0.112050221 x = 0.112050221 Simplifying x = 0.112050221Solution
The solution to the problem is based on the solutions from the subproblems. x = {249.887949779, 0.112050221}
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