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Simplifying 4x2 + -49x + 100 = 0 Reorder the terms: 100 + -49x + 4x2 = 0 Solving 100 + -49x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 25 + -12.25x + x2 = 0 Move the constant term to the right: Add '-25' to each side of the equation. 25 + -12.25x + -25 + x2 = 0 + -25 Reorder the terms: 25 + -25 + -12.25x + x2 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + -12.25x + x2 = 0 + -25 -12.25x + x2 = 0 + -25 Combine like terms: 0 + -25 = -25 -12.25x + x2 = -25 The x term is -12.25x. Take half its coefficient (-6.125). Square it (37.515625) and add it to both sides. Add '37.515625' to each side of the equation. -12.25x + 37.515625 + x2 = -25 + 37.515625 Reorder the terms: 37.515625 + -12.25x + x2 = -25 + 37.515625 Combine like terms: -25 + 37.515625 = 12.515625 37.515625 + -12.25x + x2 = 12.515625 Factor a perfect square on the left side: (x + -6.125)(x + -6.125) = 12.515625 Calculate the square root of the right side: 3.537742925 Break this problem into two subproblems by setting (x + -6.125) equal to 3.537742925 and -3.537742925.Subproblem 1
x + -6.125 = 3.537742925 Simplifying x + -6.125 = 3.537742925 Reorder the terms: -6.125 + x = 3.537742925 Solving -6.125 + x = 3.537742925 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.125' to each side of the equation. -6.125 + 6.125 + x = 3.537742925 + 6.125 Combine like terms: -6.125 + 6.125 = 0.000 0.000 + x = 3.537742925 + 6.125 x = 3.537742925 + 6.125 Combine like terms: 3.537742925 + 6.125 = 9.662742925 x = 9.662742925 Simplifying x = 9.662742925Subproblem 2
x + -6.125 = -3.537742925 Simplifying x + -6.125 = -3.537742925 Reorder the terms: -6.125 + x = -3.537742925 Solving -6.125 + x = -3.537742925 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.125' to each side of the equation. -6.125 + 6.125 + x = -3.537742925 + 6.125 Combine like terms: -6.125 + 6.125 = 0.000 0.000 + x = -3.537742925 + 6.125 x = -3.537742925 + 6.125 Combine like terms: -3.537742925 + 6.125 = 2.587257075 x = 2.587257075 Simplifying x = 2.587257075Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.662742925, 2.587257075}
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