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Simplifying 4x2 + -25x + -11 = 0 Reorder the terms: -11 + -25x + 4x2 = 0 Solving -11 + -25x + 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'. -2.75 + -6.25x + x2 = 0 Move the constant term to the right: Add '2.75' to each side of the equation. -2.75 + -6.25x + 2.75 + x2 = 0 + 2.75 Reorder the terms: -2.75 + 2.75 + -6.25x + x2 = 0 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + -6.25x + x2 = 0 + 2.75 -6.25x + x2 = 0 + 2.75 Combine like terms: 0 + 2.75 = 2.75 -6.25x + x2 = 2.75 The x term is -6.25x. Take half its coefficient (-3.125). Square it (9.765625) and add it to both sides. Add '9.765625' to each side of the equation. -6.25x + 9.765625 + x2 = 2.75 + 9.765625 Reorder the terms: 9.765625 + -6.25x + x2 = 2.75 + 9.765625 Combine like terms: 2.75 + 9.765625 = 12.515625 9.765625 + -6.25x + x2 = 12.515625 Factor a perfect square on the left side: (x + -3.125)(x + -3.125) = 12.515625 Calculate the square root of the right side: 3.537742925 Break this problem into two subproblems by setting (x + -3.125) equal to 3.537742925 and -3.537742925.Subproblem 1
x + -3.125 = 3.537742925 Simplifying x + -3.125 = 3.537742925 Reorder the terms: -3.125 + x = 3.537742925 Solving -3.125 + x = 3.537742925 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.125' to each side of the equation. -3.125 + 3.125 + x = 3.537742925 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + x = 3.537742925 + 3.125 x = 3.537742925 + 3.125 Combine like terms: 3.537742925 + 3.125 = 6.662742925 x = 6.662742925 Simplifying x = 6.662742925Subproblem 2
x + -3.125 = -3.537742925 Simplifying x + -3.125 = -3.537742925 Reorder the terms: -3.125 + x = -3.537742925 Solving -3.125 + x = -3.537742925 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.125' to each side of the equation. -3.125 + 3.125 + x = -3.537742925 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + x = -3.537742925 + 3.125 x = -3.537742925 + 3.125 Combine like terms: -3.537742925 + 3.125 = -0.412742925 x = -0.412742925 Simplifying x = -0.412742925Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.662742925, -0.412742925}
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